RAF and Commonwealth Aircrew in 2 TAF, based on the Continent after D-Day, were issued with a .38 Webley or Smith and Wesson, and some acquired the Browning HP35. These were to be worn in a standard issue webbing Service holster, on a '38 Pattern web belt. Some are known to have carried this in one of their flying boots!
(Early Spitfires had a holster on the port wall, for an Enfield pistol, although the carriage of the actual weapon seems to have been rare, and might have been more for a 'final solution' in the event of being trapped in a burning cockpit!)
However, many aircrew did not carry the weapon, for fear of being shot by the enemy, if the weapon was seen after a forced landing or bail-out.
For similar reasons, Typhoon pilots, in particular, were issued with Army Battledress blouses, onto which their rank tabs and wings etc were sewn, but in this case, it was to help prevent being shot by 'friendly fire', when the 'RAF Blue' uniform, in the heat of the moment, might have been mistaken for the grey of the Waffen SS uniform. Contemporary photos show a mixture of attire, with and without holstered weapons
In general, it was not common practice, in the RAF in the ETO, to carry a personal weapon, although this was more common, and I believe part of SOP, in the MTO and PTO.
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'Modern' RAF aircrew, if on Ops over hostile territory, carry a Browning HP35, or a H&K or Sig semi-auto pistol, in an 'arm pit' holster as part of the survival vest, with a 'release' knife in a spring-loaded, metal scabbard, which slides into a 'sleeve' on the right thigh of the Mk4 and Mk14 flying suit, but, since the introduction of the current 'US style', sage green suit, I believe this knife has been replaced by a survival-type knife, again carried in the vest, which replaced the 1970s pattern 'Frankenstein' life jacket, in service until recently.
Luftwaffe aircrew of all ranks, were issued with, and were supposed to carry on Ops, a Walther PK pistol, carried in a leather holster on the leather Service belt.