The possibility has been raised that these were the 1,000 or so American-supplied QF 75mm guns in the French style that formed some units divisional arty in mid-1940 immediately after Dunkirk, but firing solid AP shot...but just today I've come across reference that the "75mm AT" MAY have been a domestic creation after all...
Duty Without Honour , David Orr (the history of the Ulster Home Guard)The introduction of the new 3.7-inch guns (AA guns - my note) resulted in the mountings from existing 3-inch guns being required. This left the War Office with a surplus of several hundred 3-inch anti-aircraft gun barrels and breach mechanisms; also stockpiled were large numgers of gun carriages from the vintage First World War field gun, the 4.5-inch (35pdr) Field Howitzer.
These factors, together with an identified need for an anti-tank capability, provided part of the catalyst for the creation of a new weapon. In essence it was a "mongrel" creation manufactured from spare parts of other guns. The 4.5-inch Field Howitzer gun carriages were overhauled and given new wheels with pneumatic tyres, while the barrels of the old 3-inch A/A guns were shortened and mounted on the reconditioned carriages. This whole piece was then redesignated as the 75mm anti-tank gun.
In the local example, several units of the UHG took possession of 75mm AT guns at the end of 1942, as the RAF Regiment in the province was withdrawn for more active operational roles - North Africa, Italy etc. As the Home Guard took over responsiblity for guarding aerodromes here, they ALSO took over the two 75mm AT guns that provided the A/T defences on each airfield. (Later, as more became available from the UK, an extra 15 were issued to bolster the Home Guard defences of Belfast and Derry City)
At THIS point I'm presuming a similar process occured in the rest of the UK; historically from late 1940/early 1941 the Home Guard took over more and more "base establishment" duties - manning coastal defences, airfield defences, AA batteries etc. ...and that AFTER a Home Guard unit took over a defence responsibility from a Regular unit going abroad, the weapons they left behind...allocated to a location rather than the unit...appeared on the roster of the respective Home Guard unit.