I don't know what a "B-M" .45 is, but SOE used about anything they wanted. Commandos generally used Colt Government Models, the first orders being placed in 1940. Most were probably military M1911A-1 variety. I once had a Lend-Lease one. Commandos also retained the Thompson .45 SMG after regular British units went to the STEN 9mm SMG. I read this in a book on Army commandos. Royal Marine Commandos may have varied.
Until fairly recently, SAS men could use any handgun they wanted that, "could be obtained in Britain or taken from an enemy".
I read a book by or about a Lt. McHorton (sp?) who fought in Burma with the Chindits units. He had a Thompson and a Colt Official Police .38, the latter chambered in .38/200.
General officers, CID, Field Security, and pilots often use the Walther PP and PPK. The PP is favored for concealed carry in Northern Ireland.
You need to start by buying a copy of, "Small Arms of the World" by Smith and Smith. I think the last edition was the 12th or 13th.
Winston Churchill was fairly typical of officers before the Enfield .38 was adopted, after which (I read somewhere) the use of personal handguns was forbidden or discouraged. This came as the UK was adopting their increasingly more severe gun laws. Obviously, it was augmented by other types in WW II, due to the great need.
Churchill used a Wilkinson-Webley, Model of 1892, a Mauser M96 7.63mm auto, and a Colt M1911 .45 ACP, NOT a Colt .455. In WW II, he sometimes carried his Colt .45 and a Webley .38, I think a Mk. IV.
Robert Stanford-Tuck, the RAF ace, was said to prefer a Beretta .32 or .380. I'd guess he got it from someone who took it off an Italian.
It's well known that SOE and other special ops types often used German .32's or the Colt .32 auto.
Don't forget that officers bought their own guns before the adoption of the Enfield .38 and that both Colt and S&W were popular. Officially, the gun was supposed to be chambered for the issue load, but some ignored it, or owned more than one gun.
Lt. Col. Fosbery, VC, who later invented the Webley-Fosbery automatic revolver, noted in the 1880's that the best stopping power he saw on India's NW Frontier was from the Colt Frontier Model .44/40. He was quoted in John Parson's, "The Peacemaker and Its Rivals", which has long been out of print.
Lone Star