Yes, I think you've probably nailed it there - I was forgetting that Rose Bros. were in Gainsborough.
But it's also quite possible that this is a letter code for another foundry that gives no clue to its name or location, which was the purpose of such codes after all; "JG" and "N92" being the obvious examples.
Quite likely the Indian divisions "overseas" took their weapons back with them at the end of the war, it would have been a simple way of getting rid of the stuff while giving them an update over the weaponry they had before WWII.
No doubt their small arms, including No4(T)s were issued from the same sources as what the Canadians for example received, and therefore the same potpourri of manufacturers.
IIRC there's photographic evidence of No4s on issue in India by 1944/45, though can't be sure about formations without checking.