"Indeed, the airports of the southeast cannot "be closed", without their owners' consent."
The English statute book does not go back 900 years for nothing
For a start the Govt can change the rules on noise at LHR say 40dB max, then they can close the roads and railway links, they can pull the Immigration & Customs service and security. They can pass a law allowing hundreds or thousands of old claims for "Noise injuries"
They can make the area a military flying zone requiring 24 hours notice of entrance
easiest would be to allow a big tax break for converting the whole place into a housing estate ...................... BAA would close it in 24 hours............