This might be a bit out of your area (but it's reasonably easy to get to from anywhere in the South East):
North Sea Medical Centre
3 Lowestoft Road,
Gorleston,
Great Yarmouth,
Norfolk
NR31 6SG
01493 600011
I know that they're specialists in the field of medicals for offshore workers. I've been through one and I can tell you that they're very thorough! (I only needed it to work on the railways. The local rail company use the North Sea Medical Centre for all of their staff medicals, and the same tests are applied as for oil workers).
Chris