If you were going to close a London airport, now the Luton people mover is getting built I suspect Stansted would be the one. I doubt any of them will close, however, they will just operate at lower capacity than they did.
Given some of the announcements over the last week - notably of Virgin and BA effectively leaving Gatwick, I'm not sure your post has aged that well and I'd probably be more inclined to bet against Gatwick.