Surely if you've an history of asthma a lot of these suggestions are out. Before joining The Royal Navy ( many years ago) I had to have a chest X-ray a part of the initial interview. Likewise when I joined the Fire Service later. Remember wearing breathing apparatus is obligatory. I would imagine most of the services would be the same. Are you into bike racing? If you are have you thought about volunteering to help a pro race team. You could do this whilst still working (and earning) with a view to going full time into a paid career in racing.
