Ah but BACX doesn't use LHR at all!
Correct. So currently you have to drive to LHR and maybe connect to a BA long haul flight. You think BA really want to sell BACX to LH so that they can say 'Don't drive to LHR, connect from your local airport to FRA and get a big discount'? Its bad enough with KLM, BAs board are unlikely to faciliate similar competition from LH are they?
BA sold GO to Easy Jet
No they didn't, they sold GO to a finance company at a healthy profit. The finance company later sold GO to Easy.
all the bits which have been sold off have nearly instantaneously made a profit, from cargo (GSS)
Cargo has not been sold off. BA still carry vastly more tonnage in hold cargo than GSS, nor was any part of the entity that is GSS ever owned by BA, it was funded by Atlas. BA World Cargo is a very profitable division in its own right.