Asthma
Your asthma shouldnt be a problem, especially if you can play competative sports with no problems.
I also have asthma (and you need a letter from your doctor befroe you go but im guessing this is why you are seeing them?) but I had no problems passing.
One word of advice I would give you going into the medical. Wear trainers.
Because you have asthma it is more than likely they will make you run around the outside of the building 2 or 3 times before coming back in for another peak flow.
I had to do this which wasnt a problem, but I did find it funny that the person who was also doing their test that day was stood outside smoking whilst I was running around, yet they just had the normal test!