You get charged for using a credit card on Eurostar website but if I remember correctly it's £4 so definitely worth it!
As an American Express Cardmember, you are eligible to receive a £25 statement credit when you spend £100 or more at Eurostar by 31/01/15.
Offer available only when booking on Eurostar.com or at the Eurostar desk in St Pancras, Ebbsfleet and Ashford Stations. This offer cannot be used in conjunction with any other offer. Offer can be redeemed once per Cardmember. To receive the £25 statement credit, register your Card by entering your details and spend £100 or more on your registered Card.