The British Army did buy No.4s from Long Branch. They didn't use the No.4 in the Far East very much, if at all, in WWII, and the Indian Army was supplied with the No.1MkIII from Ishapore production.
I don't know if India bought Canadian Army No.4s sold surplus or new production Long Branch rifles after the war, but they likely would have acquired a lot of surplus No.4s from the British Army after WWII, and that would have included Long Branch rifles.