There is an interesting article in the Economist that argues the real answer is to let the 30% of passengers who transit Heathrow (rather than originate or complete their journey there) go elsewhere (FRA, AMS, CDG). The UK does not derive any real economic benefit from transit passengers, although BA and BAA might.
The 'Heathrow needs a third runway or the City of London dies' argument collapses if you take out transit passengers.
The logical place for Heathrows third runway is the Continent.