From that.pdf
If you suffer from asthma or have done in the past, you cannot be considered for flying branches of the RAF. For ground branches and trades, people with a past history of asthma, wheezing or inhaler use may be eligible for service following review by medical staff. If you have current asthma symptoms or a current prescription or you use an inhaler for asthma or wheeze (regardless of cause), you are not eligible to apply for service
As you're going SNCO ATC, if you can show you don't currently receive treatment, you've still got a chance. Get a new GP to say you don't suffer from it now and then go to an AFCO to get properly assessed.