We have recently moved into the area and are looking for vet who is specifically interested in cats. We are happy to travel likewise cost is not so much of an option when it comes to these little ones.
Andrew H Kirby (Grange Road) is very good. Conventional vet practice with reasonable charges.
A special mention though has to go to the Celia Hammond Animal Trust on Lewisham Way. They are a cat charity and vet practice and their animal care is second-to-none. Their customer service (by which I mean bells and whistles) isn't as good, but that's because they're inundated. They recently saved my two-year-old cat's life when another vet (not Andrew H Kirby BTW) had wanted to euthanase her. They provided Tilly with specialist treatment and I'm pleased to say she is well on the road to recovery. She was really at death's door and were it not for their intervention she wouldn't be here now.
If your cat has some sort of specialist/obscure condition then I'd say give Celia Hammond a ring. For immunisations or more routine stuff, use Andrew Kirby.
I have no affiliation with either practice other than in the guise of customer.
Andrew Kirbys has actually become Medivet, so I think Andrew must have sold up, which is a shame as he was a lovely vet. I have found the new vets just as good and the charges seem very similar, but I thought it was worth mentioning.
A friend of mine goes to pets at home, admittedly with a dog, and is very happy with them. I go to John Hankinson at New Cross, with cats, dog and rabbits, they are lovely, I am very happy with them though New Cross can be a bit of a slog.