Ok - The official line for the cheap seats!!!
Applicants must be sympton and treatment free for four years and will still be subject to a full medical and a pre-joining fitness test (1.5 miles on a treadmill for sailors), whereby if you can get over these obstacles you may be accepted for training. Fitness is and has been cranked up at HMS Raleigh in recent times, so anyone slipping through the net could well find themselves being found out. Having spoken to medics from the sickbay at raleigh in recent months this has become one of the prime reasons for discharge.
I can (and do) fully appreciate that asthmatics want to live as full lives as possible and have the same opportunities as everyone else, indeed I have great respect for anyone who is prepared to take up a career which includes a large amount of physical endeavour (at least in the short to medium term) and who suffers from such a potentially debilitating condition. That being said the service has a duty of care to it's employees and as such can take no chances with these things. Imagine suffering an unexpected attack during a firefight in Afghanistan or on deck in rough weather. Not good!