It depends on the pet!
Up to two small pets per passenger, like cats and dogs can travel with you for free, as long as they don’t annoy other passengers, or put them in danger. They must be kept on a lead, or comfortable in a closed basket, cage or pet carrier that’s secure, so they can’t escape. If you’re lucky enough to have more than two pets, you’ll need to check with the train operators you will be travelling with.
As you might expect, your pets aren’t allowed to climb on the seats. They’re for paying passengers only. Don't forget to check with the operator of all parts of your journey that animals are allowed - this includes buses, coaches and taxi's and the underground if appropriate