I have just (Apr 24) completed my Class 2 Medical (initial issue). I used Dr Ajay Kumar at Petersfield Medical Practise in Cambridge. Before attending ensure you have created a CAA Portal account (see other post in this Group) and logged into the medical app Cellma which is part of it, there you fill in an application for a test. For an initial issue this includes your medical history, and of course ~£10 for the privilege! A top tip regarding the CAA from the Dr was, if you haven't paid, it probably hasn't worked!
You will need to take your CAA number and any relevant medical paperwork such as previous CAA medicals. If you use glasses, take them and/or relevant prescription. The medical is split into 2 parts. Firstly prelims with a nurse (for initial issue: height, weight, ECG, blood pressure, eye sight test and hearing test for IR/night rating). Second part is a medical with the Dr. Goes through medical history, brief examination and sorts paperwork if all ok; you walk out with the Medical Certificate. Payment at the medical centre (£225).
I found this practise and Dr very efficient and helpful. Dr Ajay flys a Cessna out of Cambridge airport and so knows GA quite well.
As a complete asside, he mentioned Cambs airfield is due to close for re-development and the Cambs club is likely to move to Duxford.