Here is an excerpt from the RSPCA guidelines
As a minimum your dog must be able to sit and stand at full height,
turn around, stretch out and lie down in a natural position. Document
It might be argued that for a short journey, say a visit to the vet, a slightly smaller crate would be okay but in my opinion for regular travel and ...
I think the Animal Welfare Act 2006 would be the legal document ruling the treatment and housing of dogs.
Section 9 "Duty of person responsible for animal to ensure welfare" states:
(1) A person commits an offence if he does not take such steps as are reasonable in all the circumstances to ensure that the needs of an animal for which ...