Cuillin you are wrong to say he should have diverted.
If the airfield is open and weather suitable (as in this case) only a fool would set off on a diversion to intensionally make a low fuel situation more critical by burning your alternate fuel.
Given that LHR and LGW would both be likely to be suffering from delays just declare a PAN/Mayday as appropriate, get on with the approach and make a note to carry more fuel next time.
The only time this would not be sensible is if the weather is marginal at your destination and your alternate is better (which it always should be). In this case landing is not assured at your destination and you should have been on your way to to your alternate sometime ago!