As it is not a direct flight, I think there may be too many variable and open risk that they won’t let the OP fly (e.g. today extra cancellations at both LHT and LGW could mean the OP is stuck in London).

i would attempt to contact the local Greek consulate as they could issue him with a temporary Travel Document (the ones they issue at short notice to travel back home when ones lose the passport on a trip abroad).