Always shop around when you're looking for a vet (much like any business don't just accept one for the sake of it) ask lots of questions? Ask them how many Chihuahua's they have on their books, try and find a small animal specialist in your area they strangely tend to be very good with chihuahua's as well. If possible try and find one which is a veterinary hospital as opposed to just a surgery as they often run emergency clincs and are 24 hours, you always find if your dog is going to hurt itself it's almost always either a Sunday or around midnight.
Just remember if you don't like their service walk away there are plenty of vets out there you just need to find the right one for you. Also ask over the local park when you see people as to where they take their dogs, you can't get a better recommendation than word of mouth
Also the RCVS I believe has a list on their website of practices they recognise so possibly start there
EDIT: I forgot to say how we found ours, lets just say we shopped around a lot and our actual vet is within 10 minutes, one of the vets is a leading expert on guinea pigs and small animals (she was a godsend when Zero fractured his back leg) they also have very close links with RCVS and have many a chihuahua on their books and our emergency vet is Stone Lion Hospital which I've also found to be an extremely good practice not to mention the place is huge and it's open 24/7.