LHR is my home base and therefore every other landing I make is normally there.
As local crew we know the published procedures pretty well off by heart (except 09R which I've only had once in the last dozen years).
I would therefore expect to do the procedure for the actual landing runway, and not cut across potential go around traffic for the other runway. Or have vectors.
(We normally have the other runway programmed in the secondary flight plan in the FMS. A really switched on crew might get the PNF to activate the secondary flight plan when the cross over was given. They'd then have the new go around procedure in the box, having dumped the orignal one.)
Food for thought.