The perennial hub to hub railway proposal that you avoided mentioning but others have, suffers from two problems - one is the incredibly high cost of land acquisition and tunnelling, and the other is the logistical one of whether it is technically landside or airside. If it is landside, passengers will need to go through UK immigration at their arrival airport, adding lots of time to the connection.
I think you got the idea here.
UK and the rest of Europe are very different, particularly on legislation regarding to ownership. In UK ownership, particularly of land is sacred. If you own a piece of land, you may do almost whatever, like prohibiting others trespassing, even if it is an empty faraway terrain in the middle of the forest. Confiscating the land for government is very difficult and expensive, even more for a private or semiprivate company, so in practice whoever wants to build a runway, railway or highway has to offer so much money that the landowner accepts the offer voluntarily. For highways you can make a curve in the middle, if one landowner refuses to sell. For a runway it would look funny.
Add to that the poor quality of the rock which makes tunneling very expensive.
While almost every other country could connect the airports with a high speed train link (e.g. LHR-LCY & LGW-STN connecting at Trafalgar Square, and possible circular airside links) with a couple of billion Euros, in UK that would cost tens of billions £.
Andy33 wrote:If it is airside, the proponents need to explain how it is possible to maintain a secure border along 30+ miles of railway, especially in the event of trains breaking down or other incidents requiring evacuation. This certainly isn't done anywhere else in the world. Now it was done to an extent in communist East Germany for a strictly limited number of trains a day, by operating a shoot-to-kill policy, but this is scarcely acceptable in a democracy!
In the US you always change to landside when connecting, so TATL pax may not even expect airside connection, even if it would be luxury. It could be arranged, though. Even in the airport in case of a fire you will be evacuated out into non-sterile space.