As others have said, because of rabies prevention, if you take an animal out of the UK, the dog needs to have been microchipped, inocculated, and possess a pet passport, otherwise your daughter will be without her dog for 6 months while he/she is in quarantine (the dog that is, not your daughter!)when you return. Best to see your vet, as there may be a certain amount of time after the innoculation before the pet passport will be given.

You don't say whether your journey originates in London or whether you are connecting from elsewhere....