Ok, please bear in mind that what I write is only from my personal experience - if you want definative answers then the only thing to do is ask the RAF directly.
I fear that with any history of asthma, it will be more or less impossible to join as aircrew. I myself have recently been through selection at Cranwell. When I was younger I was tried on an asthma drug for a cough I had - it did nothing (i.e. I do not have asthma) but this remains on my records. Given that I was applying to be a pilot, I was required to go for specialist testing to confirm the absence of asthma - and that is for a case of suspected asthma over a decade ago. If the medical board are this stringent over someone who has never been diagnosed with asthma, it seems a gloomy outlook for anyone who has ever suffered it.
Of course, people talk on here about applying, and not telling the RAF about their diagnosies. It's worth remembering that if selected the RAF will request medical information from your GP. If this throws up anything that you have purposely failed to mention then any chance of an RAF career is effectivly gone - you have displayed a lack of integrity etc.
Speaking to one of the medical staff, I was told that one reason that the RAF has such stringent rules with asthmatics is that they have a particularly bad reaction to the Naps tablets taken to protect against the effects of chemical weapons. This is second hand knowledge though - please correct me if im wrong.