The Royal Navy has recently published online the
personnel management handbook (BR3) and the
handbook of medical standards (BR1750A)
Between the two you will find authoritative answers to all your recruitment questions.
For example, this is the para on respiratory matters:
"0503. Breathing Problems
a. Asthma. Candidates who currently suffer from asthma, or have required
treatment for asthma during the last four years, should not be accepted into the
service. Individuals who have suffered from asthma as a child may be considered but
only if they have been treatment and symptom free for at least four years.
b. Hay Fever. Mild attacks which would not affect the efficient performance of duty
may be ignored. Severe hay fever is likely to be a bar to entry, the severity being
judged by the need for prolonged medication. Hay fever in Aircrew has the potential
to cause incapacitation in flight. Aircrew candidates with a declared history of hay
fever may be considered for selection if they have had no treatment and no symptoms in the 4 years preceding their appearance at the selection Medical Board.
c. In cases where there is doubt as to the individual's fitness, they must be referred
by the AFCO ME to CAAMB with the RN Respiratory Questionnaire completed by the candidate’s general practitioner."
Edit:
Search terms: FAA, Fleet Air Arm, pilot, observer, aircrew,
don't join the Crabs, AIB, BRNC, Admiralty Interview Board, Dartmouth.