British
Rifles are preferred but SMGs are OK. Ammunition is strictly limited to ten rounds - you aren't going into battle, you are re-capturing prisoners, who unsurprisingly don't want to be killed. In the real world if someone is pointing a gun at you then you comply with commands. Shooting at distant escapees who are running away from you would be futile and you might have to account for your actions later. There is no requirement for sub-350fps guns (although this is a sensible option) - up to 500fps is fine if you have nothing else but obviously if you are going to be discharging a weapon at that power you must observe a minimum engagement distance. Killing prisoners is forbidden - this is Britain. And there is paperwork and there are political and rank/career/posting consequences to consider.
Germans
Germans have no access to weaponry(*) and didn't fire a shot in the real 'Great Escape'. However, there may be cached weapons that can be obtained via liaison with fifth columnists - this will be provided for you.
Once you have been caught then you will rejoin the game on the British side as Home Guard (if you only have civilian uniform) or Home Guard/Regular Army if you are bringing a British uniform with you. So, please bring a suitable weapon (see British above) for your secondary role if caught.
(*) Larp safe knives, axes, etc, are fine if you have them and can get close enough to use them!
If ever there was a game for shotguns, this is it. We will have to turn a blind eye to illegal shortened shotguns - don't be surprised if the local constable has a quiet word with you though!
BARs and Thompsons are fine but you will have to put up with a miserly ammunition provision. Well, there is a war on you know.
Mausers, Winchesters, hunting rifles and all manner of long guns are great. Even Great War trophy Lugers. Six shooters and flintlocks might be pushing credibility though!