Half-decent .45 ACP calibre SMG that the Yanks used in WW2, along with a load of gangsters in the twenties and thirties who liked the extent to which they could shoot the crap out of each other with it. Went through a number of changes between the first production model in 1921 (thirty-five to forty magazine-fed prototypes had been hand made in 1919, a few of which were shipped to europe,) and the guns used in WW2, but none of them did much to change the fact that it was bloody heavy.
Following Dunkirk, large amounts were acquired from the United States by government purchase and a number of private American donations, and later of course via the Lease-Lend programme.
In service originally with the Home Guard in the latter months of 1940, it was, however, of a higher manufactured quality than the Sten which the British Army first received in mid to late 1941. Apart from the financal aspect, one of the reasons for the proliferation of Stens in Brit service was the United States entry into the war in December 1941, which put greater demands on the manufacture of Thompsons for the expanding US forces. (Now watch the tinfoil hat wearers read the previous two sentences, then put two and two together to make forty-seven...)
A number of Thompsons were modified by BSA and produced as the "BSA 1926" (in 9 x 20 FFS!) but the army knew better and showed little interest. A .30 Carbine calibre variant was in existance but defied the intent of a Light Rifle, which led to the Thompson Light Rifle but also got the knock for the M1 Carbine.
Also known as the 'Tommy-gun.' Using the name for any other SMG is just wrong.