What is mind boggling is given the state of the aircraft they even considered flying back over central London.
I shouldn't really, but: The state of the aircraft ??
As far as the pilots knew, they had lost some panels but one engine was working normally. They had lost one of three hydraulic systems, and were having to fly with manual thrust. The right engine only developed a fire on finals. No great drama then for a professional flight crew, who practice such events every 6 months in the SIM. So tell me; why would they have needed to land at Brize? What was the urgency? Brize is a military airbase; do they have steps for an A319? What is the landing distance required for an overweight A319 with no yellow hydraulics? How long is Brize's runway? Was the wind at Brize within limits for landing? Would they have all their braking, antiskid, reversers, flaps and spoilers available? (I know the answers, but do you?)
Or they
could have landed at EGSS, but again; where was the urgency? If they had gone there, would there be a stand available for them? Would BA staff have been there to assist? Where would the passengers have gone and who would have looked after them? Are any BA engineers based at EGSS?
Had there been an uncontained fire, of course they would have landed at the nearest suitable runway. But there wasn't. So they didn't.
Most of the "why did they fly over London" brigade seem to be thinking of an engine failure in a Cessna 152. In that instance, you MUST find a field and land in it - you would not dream of doing anything else, and certainly would not attempt to cross a large city, (and it would be physically impossible anyway). However, modern jets with single hydraulic problems and perhaps an engine fire do not fall out of the sky. There are so many more factors a professional flight crew in charge of a modern commercial jet take into account.
What is actually mind boggling is all the armchair 'experts' who have clearly never flown a modern jet, but who think they know better than the actual flight crew who were there.