I think it is very regrettable that Concorde was vandalised as it was by Air France, BA and Airbus. I could well understand removing it from service but I could not understand why it could not have been kept flying for display purposes via a charitable trust.
As it is highly unlikely that the aircraft at LHR or indeed any other, will ever fly again, I would favour the removal of the aircraft from LHR completely.
It could either be given to a museum far from LHR and London or simply destroyed. It is after all a relic of a bygone age when BA actually led the world in aviation. They no longer do so and sadly Concorde, much like the BA of today, is a decaying emblem of a grander time.