Hi Pipergirl
I was hoping someone with more knowledge than me would post a reply to your question, but until that happens I'll have a go.
I went for my Class 1 last Thursday and received the certificate today. It's great to have it and I feel like framing it! I've had LASIK so it wasn't by any means a done deal.
Anyway, back to asthma. I don't have it, but two of my three kids do, as does my brother, so I had to report all this on the questionnaire. You'll do a peak flow test but in my understanding this won't necessarily be lower in a person with asthma if it is well controlled, e.g. through the use of steroid preventers. I did ask the doc doing the test various questions re. asthma, although not in as much detail as you might wish to. The impression I was given is that asthma is not in itself a bar to a Class 1 as long as it is controlled. If you have a record of asthma attacks leading perhaps to hospitalisation then I doubt you'll pass, but if that isn't the case then I'd imagine you'll be OK. They might endorse the certificate with a requirement that you always carry an inhaler, but that's my guess and not based on anything they said.
I was definitely left with the impression that there are commercial pilots flying with asthma.
Good luck!