Hi Stranger,
This is the link to the CAA website which lists the AME's. You can find one there.
Medical Examiners Database Search | Medical | Personal Licences and Training
I paid £90 for my class 2 medical about a month ago. But that was based in Coventry so it may be more expensive for that-there London!
Do remember though that it may cost a little more if you need "extras"! An eye examination may need to be done (although I got mine done for free in Tesco!) and a medical report from a GP may be requested if there are other things to explore. (Again, that cost me an additional £40)
Hope that helps!
Davey