LHR + Northolt + HS2 + Upper Heyford
I like the sound of one of the options/alternatives tabled earlier in this thread:
Make better use of RAF Northolt which is barely utilised - have a five mile tunnel linking LHR and Northolt underground - road and rail/M40 + M4 inner ring road effectively.
Then go and re-use Upper Heyford with a bigger junction (No. 10) on the M40 (immediately adjacent to Upper Heyford) and divert the HS2 line westwards at that stage to follow more closely the M40 - or have a spur coming off feeding that new airport. If HS2 was to take 45 minutes from London to Birmingham, it will take just twenty-something minutes from London to Upper Heyford. Ideally have HS2 go via LHR in the first place.
LHR + Northolt + HS2 + Upper Heyford then gives the industry two extra interlinked runways which already exist - no new tarmac, one of which is massive - 2.2 miles long.
It has its limitations, but (a) it's one hell of a lot cheaper than some alternatives and (b) both extra runways are the right side of London for the demand that exists and (c) one wouldn't have to wait two decades for this to be instigated - we could be there in just ten, perhaps less?