Hi Chris,
I recently wrote to the CAA concerned, as you are, about Asthma. I had a nice reply from an Aeromedical advisor telling me that my prescribed medication is acceptable (Salbutamol 100 Micrograms and Beclomethasone 100 micrograms).
The Average peak flow for my age is 610. Last time to the Asthma clinic I blew a 710. The have requested my treating physician to send them a report on my asthma, which is in the process of being done - but I expect it to be fine. I would suggest they will require the same for you.
From the research I've done, as long as your asthma is well controlled on approved medication (inhaled and not orally taken) and you have no recent hospital admissions due to your asthma, you should be fine. I used to have attacks every few days when I was about 4 or 5, now at 21 I barely notice I have asthma at all.
Good Luck!
RC