I think that Gordon Brown and crew wouldn't let Heathrow and Gatwick close. He would lean on BAA (Ferrovial) to sort it out sharpish. If LHR and LGW shut, so does the UK, right?
We had a similar threat of strike action at Birmingham a couple of years ago for the same reasons. Management couldn't afford to let the airport close and BHX has a mere 10m pax a year. BAA has 143m pax, what do you think???