The public purse has to learn to live within it's means, something no politician in recent years has contemplated. The answer is always "tax more". If the market supports an hourly JFK then well done, London and New York are two world cities. Business operates in a market that won't use STN or LGW. Either support the market or watch it move to FRA or CDG before it glances at another UK airport.
Besides which, APD is a smokescreen, all these connecting passengers create lots of jobs in baggage handling, cabin crew, cargo, back office as well as flight deck. Jobs in the real economy, not parasitic pretendy public sector jobs that serve no purpose beyond getting the underskilled into overpaid positions.
A new runway at LHR would help the economy more than building a second runway at say, MAN believe me.
A new runway will suck up resources and not solve the crowded airspace problems.
Frankly spending £2 billion on a high speed LHR-LGW would solve more of the LHR crap than building a new runway, people would question the travelling time between airports but think nothing of sitting for 35 minutes queueing once they land awaiting a gate.