Home Guard weapons varied over time. At the very beginning it was mostly civilian firearms such as shotguns and hunting rifles. The first service weapons to be generally issued were .303 Enfield Pattern 1914 rifles from reserves followed by lend lease US .30-06 Model 1917 rifles. (Sometimes designated the 'P17' in British service) The US rifles had red bands painted around them to denote they didn't take standard .303 ammunition.
As the war progressed, the Home Guard started to get more up to date weapons such as the Sten SMG. Of course, by this time the realistic chance of a German invasion had passed.
Oh, and Noel Coward penned a satirical tune on the Home Guard called 'Would you please oblige us with a Bren gun?' Many years later, it was performed by the Dad's Army cast for a Christmas special.