OK, AI did not wine, dine and entertain them which shouldn't happen.
But behind the scenes some things that are not immediately obvious;
LHR did not close due to fog, it imposed a reduced flow control. The slots for takeoff/landing were reduced meaning fewer takeoffs/landing. AI was one of the unlucky ones, perhaps they were already late or perhaps the flip of the coin, or who knows ? They diverted to Gatwick.
Once on the ground AI would appeal for a takeoff slot out of LGW and a landing slot at LHR. Eurocontrol would coordinate these requests, but with LHR already slowed down it is unlikely that they would be given anything other than "we'll do our best" , and "let us know when you are ready to go".
It is likely they would have to take on fuel, enough for the short hop, alternatives and safety margin. Once this was done they would be put into the queue for both airports, and Eurocontrol. All this time the original crew would be watching their watches. Nothing more back from EC other than we are trying our best. They might have had an opportunity at one or the other airport but they needed both.
Once the crew timed out, that was it. Eurocontrol would have said simply, too bad, but Have your replacements let us know when they are ready to go, so back to the end of the queue for you.
The crew - and it's not that likely that AI would have more than one at an out station, would then have to get from Heathrow to Gatwick, and I'm sure they did everything in their power to do that as quickly as they could. Once they were in the cockpit they would let EC know they were ready to go and they would be put back in the queue.
AI had a valid landing slot which could not be honoured. That is why everything afterwards went tits up. Of course slots are not guaranteed and Heathrow will get paid anyway once the aircraft finally arrives.