They were stationed at the Inferno Project and presumably at similar locations all over the Republic of Great Britain where they acted as an SS-like state paramilitary organisation, manning their version of the drilling project as a "scientific labour camp". They are armed with a mixture of Soviet and German weapons, such as the SKS rifle and the Walther P38 pistol while UNIT was armed with Western weaponry such as the Sterling submachine gun.
Their rank system uses titles based loosely on that of the British Union of Fascists: Sergeant Benton is Platoon Under Leader Benton, Brigadier Lethbridge Stewart is Brigade Leader Lethbridge Stewart, and Elizabeth Shaw, a soldier rather than a scientist in their dimension, has the rank of Section Leader (which appears to be an officer rank).
Their uniforms consist of contemporary US Army olive green military fatigues for Other Ranks, tan uniforms with black rank slides on the shoulders (based on the brown shirts) for officers, and black garrison caps with white piping and an RSF cap-badge as head-dress for both.
The organisation has full authority to interrogate, court-martial, and formally execute prisoners as they see fit under the "Defence of the Republic Act, 1943". By the end of the story, most of the members of the RSF are killed when a volcanic cataclysm engulfed Great Britain and left much of their world devastated.