Exhibit
4.1


THE TERMS AND CONDITIONS OF THE RIGHTS
OFFERING ARE SET FORTH IN THE COMPANY’S PROSPECTUS SUPPLEMENT DATED APRIL 21, 2021 (THE “PROSPECTUS SUPPLEMENT”)
AND ARE INCORPORATED HEREIN BY REFERENCE. COPIES OF THE PROSPECTUS AND PROSPECTUS SUPPLEMENT ARE AVAILABLE UPON REQUEST FROM BROADRIDGE
CORPORATE ISSUER SOLUTIONS, INC., THE SUBSCRIPTION AGENT, BY CALLING (855) 793-5068.


SUMMIT THERAPEUTICS INC.

Incorporated under the laws of the State of Delaware



NON-TRANSFERABLE SUBSCRIPTION RIGHTS CERTIFICATE


Evidencing Non-Transferable Subscription
Rights to Purchase Shares of

Common Stock, Par Value $0.01 per share, of Summit Therapeutics Inc.



Subscription Price: To be determined as set forth below



THE SUBSCRIPTION RIGHTS WILL EXPIRE IF NOT EXERCISED ON OR BEFORE

5:00 P.M., EASTERN TIME, ON MAY 10, 2021 (THE “EXPIRATION DATE”)


REGISTERED OWNER:


THIS CERTIFIES THAT the registered owner
whose name is inscribed hereon is the owner of certain non-transferable subscription rights (each, a “Subscription Right”).
The Subscription Right entitles the holder thereof to subscribe for and purchase shares of common stock, par value $0.01 per share
(the “Common Stock”), of Summit Therapeutics Inc., a Delaware corporation (the “Company”), at a subscription
price per full share equal to the lesser of (i) $5.24 per share (the “Initial Price”) and (ii) the volume weighted-average
price of the Common Stock for the ten (10) consecutive trading days through and including the Expiration Date (the “Alternate
Price”), pursuant to a rights offering (the “Rights Offering”), on the terms and subject to the conditions set
forth in the Prospectus Supplement, which supplements the Company’s prospectus dated October 15, 2020 (the “Prospectus”).






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Each stockholder will receive one Subscription
Right for each share of Common Stock owned as of 5:00 p.m., Eastern Time, on April 9, 2021 (the “Record Date”) and
each Subscription Right will entitle its holder to purchase 0.172598 shares of Common Stock at the Initial Price per full share.


The Subscription Rights represented
by this Non-Transferable Subscription Rights Certificate may be exercised by completing Form 1 and any other appropriate forms
on the reverse side hereof and by returning the full payment of the subscription price for each share of Common Stock in accordance
with the instructions contained herein.


This Non-Transferable Subscription Rights
Certificate is not valid unless countersigned by Broadridge Corporate Issuer Solutions, Inc., the Subscription Agent. Witness the
seal of Summit Therapeutics Inc. and the signatures of its duly authorized officers.


DATED: [•], 2021


	
   

	 	
   


	Chief Executive Officer	 	Chief Financial Officer


 


DELIVERY OPTIONS FOR NON-TRANSFERABLE
SUBSCRIPTION RIGHTS CERTIFICATE


Deliver other than in the manner or
to the addresses listed below will not constitute valid delivery.


 


	If delivering by hand or overnight courier:	 	If delivering by first class mail:
	 	 	 
	Broadridge Corporate Issuer Solutions, Inc.

Attn: BCIS IWS

51 Mercedes Way

Edgewood, NY 11717	 	Broadridge Corporate Issuer Solutions, Inc.

Attn: BCIS Re-Organization Dept.

P.O. Box 1317

Brentwood, NY 11717-0718


 


 






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PLEASE PRINT ALL INFORMATION CLEARLY
AND LEGIBLY.


SECTION 1 –
EXERCISE OF SUBSCRIPTION RIGHTS


To subscribe for shares of Common Stock
pursuant to your Subscription Right, please complete lines (a) and (b) and sign in part (c). If you do not indicate the number
of Subscription Rights being exercised, or if you do not forward the full subscription payment for the number of Subscription Rights
that you indicate are being exercised, then you will be deemed to have exercised the maximum number of Subscription Rights that
may be exercised with the aggregate subscription payment you delivered to the Subscription Agent. Fractional shares of our Common
Stock resulting from the exercise of the Subscription Rights will be eliminated by rounding down to the nearest whole share, with
the total subscription payment being adjusted accordingly. Any excess subscription payments received by the Subscription Agent
will be returned, without interest, as soon as practicable.


(a)              
EXERCISE OF SUBSCRIPTION RIGHT:


		(i)	Basic Subscription Right









	I exercise	
   

	x	0.172598	=	
   

	x	$5.24	=	
        $

	 	(No. of shares

owned)	x	(Initial ratio)	=	(No. of Basic Subscription Shares Subscribed For)	x	(Initial Price)	 	(Amount Enclosed)


 


		(ii)	Over-Subscription Right: If you fully exercise your Basic Subscription Right, above, and wish to subscribe for additional
shares, you may exercise your Over-Subscription Right below.



	I exercise	
   

	x	 	$5.24	=	
        $

	 	(No. of Over-Subscription

Shares

Subscribed For)	x	 	(Initial

Price)	=	(Amount Enclosed)


 


(b)              
PAYMENT:


	 	Amount Enclosed	 
	Basic Subscription

Right:	
        $
	 ̈    Certified check drawn on a U.S. bank, or postal or express money order payable to Broadridge Corporate Issuer Solutions, Inc., as Subscription Agent.
	 	 	 
	Over-Subscription

Right:	
        $
	 ̈    Wire transfer directly to the escrow account maintained by Broadridge Corporate Issuer Solutions, Inc., as Subscription Agent.
	 	 	 
	Total Amount

Enclosed	
        $
	 


 






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Method of Payment. All payments must
be made in U.S. dollars by wire transfer of funds, U.S. Postal money order or certified check drawn upon a U.S. bank payable to
 “Broadridge Corporate Issuer Solutions, Inc. (acting as Subscription Agent for Summit Therapeutics Inc.)”. The Subscription
Agent will not accept payment by any other means.


 


(c)               
SIGNATURE(S):


TO SUBSCRIBE: I acknowledge that I have
received the Prospectus Supplement for the Rights Offering and I hereby irrevocably subscribe for the number of shares indicated
above on the terms and conditions specified in the Prospectus Supplement. I hereby agree that if I fail to pay for the shares of
Common Stock for which I have subscribed, Summit Therapeutics Inc. may exercise its legal remedies against me.


This form must be signed by the registered
holder(s) exactly as their name(s) appear(s) on the certificate(s) or book entry or by person(s) authorized to sign on behalf of
the registered holder(s) by documents transmitted herewith.


	
   

	
   

	
   


	Signature(s) of Subscriber(s)	Date	Daytime Telephone Number(s)


 


If signature is by trustee(s), executor(s),
administrator(s), guardian(s), attorney(s)-in-fact, agent(s), officer(s) of a corporation or another acting in a fiduciary or representative
capacity, please provide the following information (please print). See the instructions.


	
    

	
   

	
   

	
   


	Name(s)	Full Title	Taxpayer ID # or Social Security #	Date


 


SECTION 2 –
SPECIAL ISSUANCE OR DELIVERY INSTRUCTIONS FOR SUBSCRIPTION RIGHTS HOLDERS


	(a) To be completed ONLY if the book-entry representing the Common Stock is to be issued in a name other than that of the registered holder. (See the Instructions.) DO NOT FORGET TO COMPLETE THE GUARANTEE OF SIGNATURE(S) SECTION BELOW.	 	
        (b) To be completed ONLY if the book-entry representing the Common
        Stock is to be issued to an address other than that shown on the front of this certificate. (See the Instructions.)

        DO NOT FORGET TO COMPLETE THE GUARANTEE OF SIGNATURE(S) SECTION
        BELOW.



 


	Print Full Name:	
 

	Print Full Name:	
 


	Print Full Address:	
 

	Print Full Address:	
 


	Taxpayer ID # or Social Security #:	
 

	Taxpayer ID # or Social Security #:	
 




 






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SIGNATURE GUARANTEE

This must be completed if you have completed any portion of Section 2.


	Signature Guaranteed:	
 


	 	(Name of Bank or Form)
	 	 
	 	 
	By:	
 


	 	(Signature of Officer)
	 	 	 


 


IMPORTANT: The signature(s) should be
guaranteed by an eligible guarantor institution (bank, stock broker, savings & loan association or credit union) with membership
in an approved signature guarantee medallion program pursuant to Securities and Exchange Commission Rule 17Ad-15.


FOR INSTRUCTIONS ON THE USE OF NON-TRANSFERABLE
SUBSCRIPTION RIGHTS CERTIFICATES, CONSULT BROADRIDGE CORPORATE ISSUER SOLUTIONS, INC., THE SUBSCRIPTION AGENT, AT (855) 793-5068
(TOLL-FREE). THE RIGHTS OFFERING EXPIRES AT 5:00 P.M., EASTERN TIME, ON MAY 10, 2021, AND THIS NON-TRANSFERABLE SUBSCRIPTION RIGHTS
CERTIFICATE IS VOID THEREAFTER.


THE RIGHTS OFFERING HAS BEEN REGISTERED
OR QUALIFIED OR IS BELIEVED TO BE EXEMPT FROM REGISTRATION OR QUALIFICATION ONLY UNDER THE FEDERAL LAWS OF THE UNITED STATES AND
THE LAWS OF THE STATES IN THE UNITED STATES. RESIDENTS OF OTHER JURISDICTIONS MAY NOT PURCHASE THE SECURITIES OFFERED HEREBY UNLESS
THEY CERTIFY THAT THEIR PURCHASES OF SUCH SECURITIES ARE EFFECTED IN ACCORDANCE WITH THE APPLICABLE LAWS OF SUCH JURISDICTIONS.



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