For an all new airport - with the aim of becoming 'London's Airport' - you are looking for an area perhaps 5 km square, pretty flat, sufficiently empty that acquisition and redevolpment as an airport won't be too big a problem or cause to much fuss, with potential flight paths for arriving/departing planes not going over too many homes, a convenient location to house workface, good communication links (which can be built if needed...) to London, the rest of the South East and and as much of the rest of the country as you can; then you need money (a lot, you'll probably have change from a trillion, but that's probably a good first estimate), political good will (again an awful lot, for a long time), etc - good luck, people have been trying to find such a site, and then the wherewithal to actually do it, for the last half or three quarters of a century, without success... As someone put it several investigations ago "An inland site is not on politically, and a coastal site is not on economically". Which doesn't give you much choice...
The bottom line is that while most people want an airport within easy reach, nobody wants one as a neighbour...