Chris,
What they asked me to do was to go to my GP and ask him to prepare a report on the history of my Asthma. Whether this falls within the NHS purview in terms of costs, I do not know. Certainly the CAA will not pay for it.
I would definately advise you to write to the CAA including a report from your GP (which itself should include your latest peak flow result). Also include a photocopy of your latest precription. You will need to be patient though, it took approximately 3 weeks for them to get back to me - I guess they are busy. I suggest you get the whole process going as soon as possible so if there is going to be any problem, you have time to figure out an alternative plan of action.
You can write to them at the following address:
Safety Regulation Group
Civil Aviation Authority
Aviation House
Gatwick Airport South
West Sussex RH6 0YR
Good Luck!
RC