It seems the consensus is, Long Branch was involved in various aspects of Bren production, on various contracts, but never actually made any receivers. Possibly they did much of the finishing work, proofing etc. on Inglis receivers at times...sound about right?
I think that description would be too generous. During the war, I suspect that SAL (LB) did it's thing while Inglis did it's own thing with the Brens, the Hipowers, the Boyes rifles, the Browning mkII AC MG gun, and the Polstens. There would be times when SAL would be assigned to provide independant testing of some of the Inglis products, but on general day to day production SAL was not involved.
Post war, Inglis started to wrap up it's small arms production and go back to making washers and dryers, while SAL converted to CAL, but still a crown corporation. So any post war small arms projects would be assigned to CAL. WRT the Brens, SAL did some of the conversions as mentioned in the thread previously, in an attempt to avoid having to buy a new weapons system. This did not work, and the C2 was produced instead. Besides being lighter than a re-worked Bren, this likely kept CAL in more work anyway.
Personally, I think the lightness of the C2 (along with it's non-quick change barrel and having to be magazine fed as opposed to belt fed) was a real negative factor for it. It was a hard rifle to control on full auto. A modified Bren had advantages, but at the same time, if the army gets a chance to have the treasury board buy new guns, it rarely says no.
Todays C9 (and it's bigger brother the C6) seem to incorporate the best of both guns and belt fed to boot.