This seems to come up on a regular basis, so a search should give lots of info.
Apparently, some authorities will allow asthma sufferers to gain a Class 1 medical, subject to certain conditions. I don't know what they are, but they are obviously depend on how bad the asthma is.
I think that it is similar to diabetes, if it can be controlled by lifestyle, and not chemicals, then you can fly. I believ that it also depends on whether you already hold a Class 1 or not.
Why don't you call CAA and ask them? Better to find out now, than later when you've already spent a whack of dosh.
Good luck. Maybe you could post feedback of what you find out.