Hi Chris,
You are right, it is possible get the Class 1 Medical with asthma. Obviously each case is different, and I'm sure it would depend on how badly you personally suffer and how under control it is.
As proof of this I myself have asthma and got through the Class 1 without any problems, and am about to start my 3rd airline job. So far none of my employers have had a problem with it, I guess it's a case of if you have the Class 1 Medical, you're fine to work for us!! I gather that some airlines (BA included) put you through medical tests of their own before offering you a job, that may be more stringent than the CAA tests, but I'm not sure of the details, you'd have to contact them yourself and ask the question.
Personally, I was wondering the same thing as yourself before I started out in this game. What I did was do the Class 1 Medical and waited until I had it in my hands before I started any plans/thoughts about doing all the training. The CAA medical department was very helpful, you should give them a call. I was told that it wouldn't necesarilly rule out gaining a Class 1, but that to pass the lung tests, I would have to do the test once, then run round the building and do it again, just to see how different the results were. As it turned out on the day, my first test was so good that I never had to do the running round the building bit (I was a little fitter in those days!!).
My asthma is fairly mild now (it was worse when I was a child) and kept well under control by inhalers, I guess if yours is a more serious case it might prove more difficult. Anyway, it can't harm doing the Medical and finding out. That's what I did - I'd always assumed I'd fail, but I didn't want to get to 60 and wonder "how would my life have turned out if I'd gone for that medical 35 years ago?" Fortunately I passed and it has saved me from having to sit in a London office for the rest of my life!!
At the end of the day however, you'd be best off contacting the CAA Medical Department at Gatwick, rather than listening to my ramblings and getting your hopes up.
Anyway, best of luck to you Chris. Let us know how you get on.
Cheers
Billy M