As far as I was aware NATS doesn't have a medical centre. The Beehive Medical Centre at Gatwick is operated by the CAA and is a totally different section from NATS, and thus run as a separate operation. I think all the doctor's who work at the centre's (LACC/LTCC/EGLL etc) are all CAA Medical Branch employee's, nothing to do with NATS, they just follow NATS guidelines.