If you have BUPA or PPP through work they do a range of health checks/medicals. I think you can also just pay to have one done through them, maybe phone one of the clinics and ask. (My husband gets BUPA through work and he has paid for additional ones for me). To be honest most of the stuff they cover a GP would do for you, (blood tests, blood pressure, reflexes, mole checks) or you are entitled to at certain ages through the NHS anyway (bowel cancer screening or mammograms). I don't think they would do a full body scan, they are very expensive.
Or maybe phone Parkside Hospital in Wimbledon and ask them.