If you're happy to travel to Cambridgeshire, you could board your yorkie with my breeder who offers boarding at a small fee. They're a family of Yorkie nuts (they have 15!) and all are kept under foot in their home (not cages). Let me know if you want her details, and I'll pm you them. She's a doll and she absolutely dotes on this breed and has an excellent line in pedigrees too if you're interested in a great pup. She's a show breeder and her dogs are gorgeous and very healthy
And yup, dogs are allowed on trains in britain. We carry Badger but we take a carrier for him when we go down to Devon so he has somewhere for a little kip if he needs it. All British Rail and suburban train services are totally fine with dogs so you'll be able to take your baby to Wales no problem (but take a carrier anyway with some of it's bedding, toys, etc. and don't forget to include water, food and so on...)