GFW, just to close the RAF side of things, the limiting medical criteria, set out in law include:
"you suffer from asthma, or have done in the last four years"
"If you suffer severe allergic reactions that mean you need to take adrenaline injection precautions, you cannot join the RAF. You cannot join if you have a nut allergy."
http://www.raf.mod.uk/careers/istherafforme/health.cfm
The British Army is rather coy about medical standards
There are many medical conditions that are not compatible with Army service. Recruiting staff have access to this information, but generally, you should not have a medical history of any problem that interferes with a physically and mentally demanding occupation or is likely to be made worse by it.
Your application will be rejected if you fail to meet the minimum acceptable medical standard for entry.
http://www.armyjobs.mod.uk/RegularAr...sical/Soldier/
The Royal Navy is more forthright but does not make specific mention of nuts.
http://www.royal-navy.mod.uk/server/...changeNav/3533
Then nearer home there is this:
People with asthma are excluded from some occupations, including service in the Australian Defence Force, and asthma can be exacerbated by some occupations, making it desirable to identify currently active asthma and assess its severity in potential entrants
http://www.defence.gov.au/dpe/dhs/in...3_2_77-85.html