Amendment to Letter Agreement, dated May 24, 2021, between Bicycle Therapeutics plc and Citibank, N.A

Exhibit 4.1

AMENDMENT to letter agreement

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This Amendment to Letter Agreement (this “Amendment”) is effective as of May 24, 2021, by and between Bicycle Therapeutics plc, a public limited company incorporated under the laws of England and Wales (the “Company”), and Citibank, N.A., a national banking association organized and existing under the laws of the United States of America (“Citibank” and, together with the Company, the “Parties” and each a “Party”). All capitalized terms used but not defined herein shall have the meanings assigned to such terms in the Letter Agreement (as defined below).

Recitals

A.The Parties previously entered in that certain Letter Agreement, dated as of July 1, 2020, and as amended on October 27, 2020 (the “Letter Agreement”), pursuant to which the Parties agreed, inter alia, to certain terms and conditions with respect to the Deposit Agreement, the Sales Agreement, and Program Sales.

B.Section 6(e) of the Letter Agreement provides that the Letter Agreement may not be modified or amended except by a writing signed by each of the Company and Citibank.

C.Each of the Company and Citibank now desires to amend the Letter Agreement as set forth herein.

Agreement

In consideration of the foregoing and for other good and valuable consideration, the receipt and adequacy of which is hereby acknowledged by each Party, the Parties agree as follows:

(a)The first sentence of the second full paragraph of the Letter Agreement is hereby amended and replaced in its entirety with the following:

“The Company has, upon the terms set forth in the Sales Agreement, dated as of June 5, 2020 (the “Sales Agreement”), by and among the Company, Cantor Fitzgerald & Co. (“Cantor”) and Oppenheimer & Co. Inc. (“Oppenheimer” and together with Cantor, the “Agents”), agreed to issue and sell through the Agents, each acting as agent and/or principal, ADSs (the “Program ADSs”), each Program ADS representing one (1) fully paid Share, with such Program ADSs having an aggregate offering price of up to U.S. $225,000,000 (the “Program Offer”).”

(b)The relevant portion of clause (i) of Section 4 of the Letter Agreement shall be amended to read as follows:

“(i) at the time of execution of this Letter Agreement, on October 27, 2020, and on May 24, 2021”

(c)The first sentence of the first full paragraph of Exhibit A to the Letter Agreement is hereby amended and replaced in its entirety with the following:

“Reference is made to (i) the Deposit Agreement, dated as of May 28, 2019, as amended and supplemented from time to time (the “Deposit Agreement”), by and among Bicycle Therapeutics plc, a public limited company incorporated under the laws of England and Wales and its successors (the “Company”), Citibank, N.A., a national banking association (“Citibank”) organized and existing under the laws of the United States of America, as Depositary (the “Depositary”), and all Holders and Beneficial Owners of American Depositary Shares (the “ADSs”) issued thereunder, and (ii) the Letter Agreement, dated as of July 1, 2020, as amended on October 27, 2020, and on May 24, 2021 (the “Letter Agreement”), by and between the Company and the Depositary.”

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Exhibit 4.1

In Witness Whereof, the parties hereto have executed this Amendment to Letter Agreement as of the date set forth in the first paragraph above.

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In Witness Whereof, the parties hereto have executed this Amendment to Letter Agreement as of the date set forth in the first paragraph above.

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