I have had asthma since year dot, and found out the hard way that it is incompatible with the military and even a VGS gliding medical.
However I wrote to the CAA and was asked to forward a GP letter and Recent Spirograph (lung fucntion graph) and was told it was acceptable so £422 later for the initial I was/am the proud owner of a JAA Class 1 without any restrictions. I didn't even have to do any running test.
I only use Seretide 50 once a day now which is very effective for me.
OK so Yes it is possible but
1. I prepared by going to the gym and doing lots of cardio, gently at first though.
2. I now run 4 miles about 3 times a week and boy can I feel the difference!
So swim, cycle or run or whatever that gets your lungs working. Don't need to go mad but certainly train them!!
Practice peak flow techniques on a PF meter - they're maybe a couple of quid on prescription.
Go to your doctors and get a spirograph done on a regular basis to see the improvement.
I was classed as having the worst asthma as a kid and was in hospital often with all the most potent meds but prepare and you shouldn't have a problem.
PM me if you want more information.