This is all very well, but Ferrovial makes good money running LHR. When ordered to sell two of its south east airports, LHR was not even considered. Why would a such a large business park on the LHR site be successful without a local airport? Maybe it could revert to being Hounslow Heath: a bit of green belt to replace that which would be lost in Kent/Essex with the associated infrastructure of the island airport.
Much of the business/industry in West Middlesex, and indeed in the wider Thames valley, is there because of proximity to LHR. Without it, the area could become a series of dormitory towns like the Essex commuter belt on the other side of London, and a "Thames valley gateway" regeneration programme may be needed as well as the existing "Thames gateway".
Before Ferrovial could be bribed or cajolled into selling LHR, or subject to a compulsory purchase order, etc., the alternative has to be up and running. So WHO PAYS?
Let's be realistic, even if the Thames airport is technically, architecturally and geologically feasible (which it probably is), it is a commercial, financial and political non-starter.
A second runway at LGW is prohibited. The very powerful anti-airport lobby there achieved a binding agreement to prevent airport expansion there for 40 years. this expires in 2019. LGW expansion is fraught with difficulty, and will not solve the lack of capacity at the national hub, LHR.
So there is only one answer: a third and fourth runway at LHR and associated expansion. With no capacity constraints a percentage of slots could be reserved to allow a return of “thinner“ domestic routes, much needed new destinations would become available, and increased frequency (on some routes) could be achieved. Aircraft will be much quieter and cleaner by the time the new runways are in use, it's already happening with the B787 and the A350.