I'd be interested to see a list of airlines that have moved "around the London airport circuit" in recent years. I bet the list isn't that long.
Airlines don't up sticks for no reason. Financially, there are consequences to moving from airport to airport. I dare say its not something done on a whim. Obviously its far easier and cheaper to increase/reduce routes.
Off the top off my head...
El Al - Stansted to Luton - A big Jewish presence in North London. Far better transport links to Luton from that part of London.
Blue Air - Stansted to Luton
Air Berlin - Stansted to Gatwick to Stansted
Aer Lingus Regional - Luton to Southend?
Air Asia X - Stansted to Gatwick to Outside London
easyJet and Ryanair rotate routes on a regular basis.