It makes me laugh how some here live in their own little dream worlds. The chances of BA buying GB or BMed are so remote. As Oxidant points out, these companies operate as a franchise for BA. The reason BA doesn't dervice the destinations with it's own aircraft is cost. BA can't operate these routes and make the profits (if some of them are?) that these two companies can. So to incorporate them in to BA would be a complete 'No Brainer'!
The nearest that you could hope to become as far as inclusion within BA would be for them to buy either the company outright but keep it operating separately e.g. like CitiExpress was. Or to invest a large stake in the company, such as 51%. Either way there would be no merging of seniority lists and no sudden hikes in T & C's. Sorry to burst that bubble but that's reality for you.
Personally though, I think that both of the above are way off the mark from WWs plans. I don't think that BA are in the market for investing in airlines at this time. I think they have much bigger fish to fry such as sorting out all the problems with the ground side of things at Terminal 4 where customers and staff are become disillusioned with the ground handling and vicariously with BA for the hours they spend waiting for bags or tugs etc. The last few flights I've operated have been delayed by 2 hours because of this. Connecting passengers just won't want to fly again with BA if this continues much longer. This inside problem has to be hurting BA, BMed and GB.