http://www.raileasy.co.uk/go/terms-and-conditions/national-conditions-of-carriage/appendix
Animals
11. You may take dogs and small animals with you into the passenger accommodation of trains. Animals, with the exception of blind or deaf persons’ assistance dogs at the discretion of the steward, may not be taken into buffet or restaurant cars. Animals are not generally allowed in sleeper compartments, however dogs may be conveyed in sleeper cabins with the permission of the Train Company. You should apply for such permission at least 48 hours before you travel.
12. Except for dogs, animals must be conveyed in a fully enclosed basket or pet carrier designed for this purpose with dimensions not exceeding 85 x 60 x 60 cm. Baskets and pet carriers must be large enough to allow the animal to stand and lie down in comfort. Animals which are too large for a basket or pet carrier with dimensions 85 x 60 x 60 cm may not be conveyed by train.
13. Two animals may accompany you on trains free of charge.
14. A fee not exceeding half the adult fare for your journey is charged for each additional animal in excess of a passenger’s free allowance.
15. An animal may be conveyed in a train’s luggage van, if one is available. A dog should be muzzled and its lead securely fastened as directed by Train Company staff. Baskets and pet carriers must be secure. Dogs and any baskets or pet carriers must be clearly labelled with your name, address and destination station. Staff will not hand over animals until you have proved ownership.
16. Dogs must be kept on a lead throughout your journey; other animals must not be taken out of their baskets or pet carriers. If your dog or other animal causes a nuisance or inconvenience to other passengers you may be asked to remove it from a train or railway premises by the Train Company or Rail Service Company staff.