Merger of Imperial AW and British AW Ltd at the end of 1939 had been agreed before the war but by the time it was carried out both carriers' services, being international only, had either been suspended, or become a quasi-military operation, and the bulk of the staff had gone into the forces. Ironically the few UK domestic civilian services which remained through the war, to outlying islands etc, remained independent outside this merger.
Quite why BSAA was set up as a separate state-owned intercontinental operation is just one of those mysteries. Would't be surprised if Bennett had just strongarmed some civil servants into it. I'll probably get some comments if I say it was a shambolic operation from beginning to end, but I'll say it anyway.
BEA really started as an offshoot of BOAC operations, and some staff were transferred across to begin with. Other independent carriers were merged/forced to merge with it. Railway Air Services, which had continued some minor operations through the war and was expanding again, though just domestic services, was one of these. It was owned mainly by the major railway companies, who themselves were about to be nationalised, with a minority interest by Imperial, which had come down to BOAC.