From my own experience, outsourced ground handling is never as good as I house. There is no loyalty to the airline and often very little knowledge of policy etc. It can be a case of "I work for circus air, not BA!". Now this isn't always the case, but unfortunately it happens a lot.
As mentioned already, BAs operation in LHR is already split across LHR with the BD acquisition. Moving a significant amount of LGWs flight to LHR would be a logistical mess.
As it has been said, that LGW is loss making, over and over again, they obviously need to do something. Outsourcing a lot of the ground will cut costs, but I think they also need to focus on their strong points; long haul leisure