Exhibit 5.1

Our ref: 20456/15489949

Dear Sirs

Registration Statement on Form S-3

1.     Background

        We have acted for Adaptimmune Therapeutics plc, a public limited company incorporated under the laws of England and Wales (the "Company"), as its legal advisers in England in connection with the registration statement on Form S-3 (the "Registration Statement") to be filed on or about 12 July 2018 by the Company with the U.S. Securities and Exchange Commission under the U.S. Securities Act of 1933, as amended (the "Securities Act"), and the rules and regulations promulgated thereunder (the "Rules"). The Registration Statement relates to the offering, issuance and sale by the Company from time to time of an indeterminate numbers of ordinary shares of £0.001 each in the Company ("Ordinary Shares"), as may from time to time be offered and sold at indeterminate prices pursuant to the Registration Statement. The Ordinary Shares are to be offered or sold in the form of American Depositary Shares ("ADSs"). Each ADS represents 6 Ordinary Shares.

        We understand that the Ordinary Shares are not, nor are intended to be, admitted to trading on any market or exchange, or otherwise listed, in the United Kingdom.

        In connection with the Registration Statement, we have been asked to provide an opinion on certain matters, as set out below.

2.     Examination and enquiries

(a)

For the purpose of giving this opinion, we have examined:

(i)

a copy of the Registration Statement (excluding its exhibits and any documents incorporated by reference into the Registration Statement); and

(ii)

a certificate dated 12 July 2018 signed by the company secretary of the Company (the "Officer's Certificate") relating to certain factual matters and having annexed thereto copies (certified by the company secretary as being true, complete, accurate and up-to-date in each case) of the following documents:



(A)

the Company's certificate of incorporation, certificate of incorporation on re-registration, memorandum of association and articles of association; and



(B)

minutes of a meeting of the board of directors of the Company held on 11 July 2018 at which it was resolved, inter alia, to approve the filing of the Registration Statement with the U.S. Securities and Exchange Commission.

(b)

For the purpose of giving this opinion, we have:

(i)

on 12 July 2018 made an online search of the register kept by the Registrar of Companies in respect of the Company (the "Company Search"); and

(ii)

made a telephone enquiry in respect of the Company of the Central Index of Winding Up Petitions on 12 July 2018 at 11:35 a.m. (BST) (the "Telephone Search", and, together with the Company Search, the "Searches").

(c)

For the purposes of giving this opinion, we have only examined and relied on those documents and made those searches and enquiries set out in paragraphs 2(a) and (b) respectively. We have made no further enquiries concerning the Company or any other matter in connection with the giving of this opinion.

(d)

We have made no enquiry, and express no opinion, as to any matter of fact. As to matters of fact which are material to this opinion, we have relied entirely and without further enquiry on statements made in the documents listed in paragraph 2(a).

3.     Assumptions

(a)

In giving this opinion we have assumed:

(i)

the genuineness of all signatures, seals and stamps;

(ii)

that each of the individuals who signs as, or otherwise claims to be, an officer of the Company is the individual whom he or she claims to be and holds the office he or she claims to hold;

(iii)

the authenticity and completeness of all documents submitted to us as originals;

(iv)

the conformity with the original documents of all documents reviewed by us as drafts, specimens, pro formas or copies, and the authenticity and completeness of all such original documents;

(v)

that the meeting referred to in paragraph 2(a)(ii)(B) (Examination and enquiries) was duly convened, constituted and held in accordance with all applicable laws and regulations; that in particular, but without limitation, a duly qualified quorum of directors was present throughout the meeting and voted in favour of the resolutions; and that each provision contained in the Companies Act 2006 or the articles of association of the Company relating to the declaration of directors' interests or the power of interested directors to vote and to count in the quorum was duly observed;

(vi)

that the minutes referred to in paragraph 2(a)(ii)(B) (Examination and enquiries) are a true record of the proceedings of the relevant meeting and that each resolution recorded in those minutes has not been amended or rescinded and remains in full force and effect;

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(vii)

that the directors of the Company acted in accordance with ss171 to 174 Companies Act 2006 in approving the resolutions recorded in the minutes referred to in paragraph 2(a)(ii)(B) (Examination and enquiries); and that all actions to be carried out by the Company pursuant to those resolutions are in its commercial interests;



(viii)

that there are no provisions of the laws of any jurisdiction outside England and Wales that would have any implication for the opinions we express and that, insofar as the laws of any jurisdiction outside England and Wales may be relevant to this opinion letter, such laws have been and will be complied with;



(ix)

that each consent, licence, approval, authorisation or order of any governmental authority or other person which is required under any applicable law in connection with the transactions contemplated by the Registration Statement, has been or will have been obtained and is or will be in full force and effect;



(x)

that the Company is and will at all relevant times remain in compliance with all applicable anti-corruption, anti-money laundering, anti-terrorism, sanctions, exchange control and human rights laws and regulations of any applicable jurisdiction;



(xi)

that no agreement, document or obligation to or by which the Company (or its assets) is a party or bound and no injunction or other court order against or affecting the Company would be breached or infringed by the performance of actions to be carried pursuant to, or any other aspect of the transactions contemplated by, the Registration Statement;



(xii)

that the information disclosed by the Searches is true, accurate, complete and up-to-date and that there is no information which, for any reason, should have been disclosed by those Searches and was not;



(xiii)

that the Company and each party to whom any Ordinary Shares are offered, issued and/or sold will comply with all applicable laws (for the avoidance of doubt, as in force at all relevant times) with respect to anything done by any of them in relation to the Ordinary Shares, including without limitation the Financial Services and Markets Act 2000, Directive 2003/71/EC of the European Parliament (as implemented in the United Kingdom) and Regulation (EU) No. 596/2014 of the European Parliament;



(xiv)

that the Ordinary Shares will be duly allotted by the board of directors of the Company in accordance with the Company's articles of association (for the avoidance of doubt, as in force at all relevant times) and pursuant to (A) a valid authorisation under s551 Companies Act 2006 and (B) a valid power under s570 Companies Act 2006 to allot the Ordinary Shares as if s561 of that Act did not apply to the allotment; and that those sections of the Companies Act 2006 will continue in force unamended at all relevant times;



(xv)

that as at each date on which the Company allots and/or issues any Ordinary Shares, the documents examined, and the results of the searches and enquiries made, as set out in paragraph 2 (Examination and enquiries), would not be rendered untrue, inaccurate, incomplete or out-of-date in any relevant respect by reference to subsequent facts, matters, circumstances or events;



(xvi)

that as at each date on which the Company allots and issues any Ordinary Shares, the Company will have received the aggregate consideration payable for those Ordinary Shares as "cash consideration" (as defined in s583(3) Companies Act 2006), such aggregate consideration being not less than the nominal value of those Ordinary Shares; and that s583 Companies Act 2006 will continue in force unamended at all relevant times; and



(xvii)

that there is and will be no fact or matter (such as bad faith, coercion, duress, undue influence or a mistake or misrepresentation before or at the time any agreement or

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instrument is entered into, a subsequent breach, release, waiver or variation of any right or provision, an entitlement to rectification or circumstances giving rise to an estoppel) and no additional document between any relevant parties which in either case would or might affect this opinion and which was not revealed to us by the documents examined or the searches and enquiries made by us in connection with the giving of this opinion.

(b)

In relation to paragraph 3(a)(xii), it should be noted that this information may not be true, accurate, complete or up-to-date. In particular, but without limitation:

(i)

there may be matters which should have been registered but which have not been registered or there may be a delay between the registration of those matters and the relevant entries appearing on the register of the relevant party;

(ii)

there is no requirement to register with the Registrar of Companies notice of a petition for the winding-up of, or application for an administration order in respect of, a company. Such a notice or notice of a winding-up or administration order having been made, a resolution having been passed for the winding-up of a company or a receiver, manager, administrative receiver, administrator or liquidator having been appointed may not be filed with the Registrar of Companies immediately and there may be a delay in any notice appearing on the register of the relevant party;

(iii)

the results of the Telephone Search relate only to petitions for the compulsory winding up of, or applications for an administration order in respect of, the Company presented prior to the enquiry and entered on the records of the Central Index of Winding Up Petitions. The presentation of such a petition, or the making of such an application, may not have been notified to the Central Index or entered on its records immediately or, if presented to a County Court or Chancery District Registry, at all; and

(iv)

in each case, further information might have become available on the relevant register after the Searches were made.

4.     Opinions

(a)

On the basis of the examination and enquiries referred to in paragraph 2 (Examination and enquiries) and the assumptions made in paragraph 3 (Assumptions) and subject to the qualifications set out in paragraph 5 (Qualifications), we are of the opinion that:

(i)

the Company is a public limited company duly incorporated under English law;

(ii)

the Company Search indicates that the Company is validly existing and does not reveal any order or resolution for its winding up or any notice of the appointment of a receiver, administrative receiver or administrator in respect of it or any of its assets. The Telephone Search does not reveal that any petition for the winding-up of the Company has been presented, that any application for administration of the Company has been made or that any notice of appointment, or of intention to appoint an administrator, has been filed in respect of the Company; and

(iii)

in connection with a relevant issuance, upon receipt of the aggregate consideration for Ordinary Shares and entry of the names of the appropriate persons in the Company's register of members, the relevant Ordinary Shares will be validly issued, fully paid and no further amount may be called thereon.

(b)

For the purpose of paragraphs 4(a)(i) and (ii):

(i)

"duly incorporated" means that the requirements of the Companies Act in force at the date of incorporation of the Company in respect of registration and all matters precedent and

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incidental to it have been complied with by the Company and that the Company is authorised to be registered and is duly registered under that Act; and

(ii)

"validly existing" means that the Company is subsisting at the date of this opinion and has not been struck off the register kept by the Registrar of Companies, dissolved or ceased to exist by reason of any merger, consolidation or limitation on the duration of its existence.

(c)

For the purpose of paragraphs 4(a)(iii), a "relevant issuance" means an allotment and issue of Ordinary Shares in accordance with the assumptions made in paragraph 3 (Assumptions) and in particular but without limitation those assumptions in paragraphs 3(a)(xiv) and (xvi).

(d)

This opinion is strictly limited to the matters expressly stated in this paragraph 4 and is not to be construed as extending by implication to any other matter.

5.     Qualifications

(a)

The opinions set out in paragraph 4 (Opinions) are subject to the qualifications set out in the remainder of this paragraph 5.

(b)

We express no opinion as to matters of United Kingdom taxation or any liability to tax (including, without limitation, stamp duty and stamp duty reserve tax) which may arise or be incurred as a result of or in connection with the Ordinary Shares or the transactions contemplated by the Registration Statement, or as to tax matters generally.

(c)

The opinion set out in paragraph 4(a)(iii) (Opinions) relates only to Ordinary Shares offered or sold from time to time pursuant to the Registration Statement that are new Ordinary Shares issued by the Company from time to time following the date of the Registration Statement. We express no opinion in respect of any securities of the Company existing at the date of this opinion which may be offered or sold from time to time pursuant to the Registration Statement.

6.     Law

(a)

This opinion and any non-contractual obligations arising out of or in connection with this opinion shall be governed by, and construed in accordance with, English law.

(b)

This opinion relates only to English law (being for these purposes, except to the extent we make specific reference to an English law "conflict of law" (private international law) rule or principle, English domestic law on the assumption that English domestic law applies to all relevant issues) as applied by the English courts as at today's date, including the laws of the European Union to the extent having the force of law in England.

(c)

We do not undertake or accept any obligation to update this opinion to reflect subsequent changes in English law or factual matters.

(d)

We express no opinion as to, and we have not investigated for the purposes of this opinion, the laws of any jurisdiction other than England. It is assumed that no foreign law which may apply to the matters contemplated by the Registration Statement, any document or any other matter contemplated by any document would or might affect this opinion.

        We hereby consent to the filing of this opinion as an exhibit to the Registration Statement. In giving such consent, we do not admit that we are in the category of persons whose consent is required under section 7 of the Securities Act or the Rules.

Yours faithfully

/s/ Mayer Brown International LLP

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Exhibit 5.1