I don't understand what is the point of keeping ground handling in-house if you don't offer services to third party airlines. As it has been mentioned before the only way I see BA outsourcing the ramp (in LHR) is to find a partner like Easyjet has done in Luton. In JFK I read that BA outsourced the ramp to Evergreen Eagle (I think).
By the way what is going to happen to the BA staff in other airports with the sale of BA Connect? Are Flybe going to provide ground handling or are they going to outsource it. The sale of BA Connect could be seen as the start of the outsourcing of the ground services.