Taking a step back and looking at the bigger picture, surly it would be more sensible to look further afield across the country instead of just focusing on London's airports? The HUGE investment required for a brand new airport would surly be better spent on providing the infrastructure for the airports we already have but are struggling eg. Doncaster - Opened in 2005, the 3rd longest runway in the UK (sufficient length for A380's) and perhaps some others up north.
It is a common place perception that for anyone living up north wanting to further than eg. Spain, then (with the exception of Manchester) they have to travel south to a London airport.
If the infrastructure was there, then perhaps the northern airports would be able to alleviate a lot of the congestion from London's airports for only a fraction of the cost of a brand new airport?