I believe that Mil' ATCOs have to have the same CAA Class One/JAA Class 3 Medical certificate as civillian ATCOs which can be issued by the CAA Medical Branch, an authorised civilian AME or the military equivilant.
You need to refer to:
Aeromedical Centre
Aviation House
Gatwick Airport South Area
Gatwick
West Sussex RH6 0YR
Telephone: 01293 573700
As far as I am aware, rank doesn't matter, Air Vice Marshalls need the same medical standards as the bog washer if they want to hold a Class One medical.