There is a huge range of experience with vets so be careful to find out if the one you choose has regular experience with them. Go for that experience above cost every time. I had one tell me Joe was female... and he was all full grown male at the time - no doubts!
Don't know which part of London you're in, but mine is in Maidstone and the kind of vet others call when they're not sure about torts in their care - Trinity Vet Centre
The Tortoise Table has a list of UK vets here that's a good starting point.
Personally, unless there is a concern I would save your money and avoid the cost of a vet. A healthy tort is growing steadily (if not full grown), feels heavy for its size, has bright shiny eyes and is eating well.
Photos of beak and claws posted here will allow others to tell you whether or not they need trimming