Apaddy
Stand allocation in T1 and T4 is done by BA, so no excuse there.
However, the constraint with LHR is simply the small size of the real estate and the various other constraints on the stands available. LHR may look large, but compared to say LAX or DFW, it's tiny.
It's a tough job and having an insight into the details of it, I would accept a dom stand and bussing, although it would irritate me if it happened at the end of a delayed flight.