Full compensation provided the reason for the delay is a qualifying one. WZ v Austrian makes clear that in the event of a diversion, it's your actual arrival time at the contracted destination (LHR in your case), or another nearby destination that's mutually agreed, which counts for the purposes of EU/UK261.

Given that the aircraft arrived on stand at LGW circa 00:18, 2h23m after the scheduled arrival time at LHR, it's clear that you couldn't possibly have reached LHR less than 3 hours late.

However, I wouldn't rate your chances of getting BA to pay up easily as high. They may well try to compare the arrival time at LGW to the scheduled arrival at LHR and claim "it was less than 3 hours late". Well yes - at the wrong airport... So it may be one that has to be escalated to CEDR.

Anyway, put in a claim - including any duty of care expenses (food/non-alcoholic drinks during the wait at MXP if you didn't have lounge access) and your expenses in getting from LGW to LHR (or nearby) - and see what they come back with.