Similar to graraps I was thinking why not to create a direct rail connection from LHR to some other airport (LGW seems an obvious choice) and move some European flights there. You'll get to Gatwick just as fast as to LHR from London, and if connecting pax could use a dedicated rail link that would be just as convenient as the FCC now I would expect this to cost less than another LHR runway as well. And the next step would be to increase capacity at the other airport, which should be much easier as it isn't surrounded by motorways and houses...