Brian
You might want to try the Combined Military Services Museum at Maldon in Essex Combined Military Services Museum You can probably catch a train there from London (48 miles). It has a massive collection of military firearms, ordnance, grenades, spy equipment. Much of the collection comes from the old MOD Donnington collection. I would rate it as a close 2nd to the National Firearms Collection at Leeds. Check the times for opening.
Nigel