hi matt
I am currently serving aircrew and had a history of asthma in the family before i joined, although hadn't had any attacks. My initial medical was borderline and i scraped through, although i was economical with the full story regarding the family history.
5 years in i failed the respiratory tests, but got my med cat back after extensive testing and about 4 months of agro.
The bottom line is you will have to pass a peak flow test and achieve a FEV1 mark of 70% or more (ask your doctor about this).
Bear in mind if you tell them about your asthma they will dig deep which can cause problems. I kept quiet, but nearly lost my med cat 5 years later, so it's a double edged sword.
As far as a civvy medical was concerned, my experience was that the CAA were very hard-lined about it whereas the military were more flexible (and they still are with me as i still can't pass the test!).
Either way, good luck!
VP