I think that if you compare house prices in Putney or Richmond with Deptford and New Cross you'll find that high levels of aviation noise is not a major concern for home owners in London. Not that it isn't an issue, just that there are more serious issues that impact how desirable an area is.

My preference is for an expansion to Gatwick. If this impacts our ability to be a major hub then the solution would be a high speed link between Heathrow and Gatwick.
Cost of expanding Gatwick is £8bn (privately funded)
Cost of a 3rd runway at Heathrow £17bn (£6bn from the taxpayer)
Cost of new airport and infrastructure in Thames Estuary £24bn

Since Crossrail cost £15bn, a high speed point to point connection between the two airports should be possible to achieve for significantly less. For connection times consider that the 44 miles from Ashford to Calais takes 30 minutes. A 25 mile connection between Gatwick and Heathrow could be achieved in under 20 minutes - the same time it takes to travel from Heathrow terminal 1 to Heathrow terminal 5!

A high speed rail link from Gatwick to Heathrow has to be better value for money, less subjected to global warming, and allowing greater airport capacity, than a estuary airport.