Asthma is becoming increasingly prevalent, and so treatment is getting more effective these days. However, it covers a very broad spectrum of severity from mild breathlessness to major breathing difficulty leading to blackout and even death. While the milder forms can be completely manageable with medication, you can understand why airlines and militaries are extremely careful about employing pilots with any history of the disease when it can be so debilitating.
The CAA is obviously the first port of call if you have a query on the ramifications of an asthma diagnosis. Your GP is of little or no use when it comes to an opinion about whether asthma will affect your employment prospects. It would probably be worth your while to have a look in the Medical forum; I have no doubt the subject has come up before.
Scroggs