I think the airfield congestion but at LHR is the main issue.
the place is completely packed out as is and with probably two thirds of the BA fleet airborne or away from home sat any time where on earth would you find space to park and other aircraft. At LHR its basically the gates plus relatively small areas at the BA engineering base. No disused runways long closed taxiways or an old adjoining decommissioned military base that many airports have.
Also would BA have to pay to park aircraft at the engineering bases I always assumed that was their property or if it belongs to HAL then BA pay rental for the who;e area they sue whether its got anything parked on not. Still with 30,000 staff furloughed their are probably a few carpark spaces