I read the article in the Times and as someone pointed out somewhere in the paper the one thing Gatrow (or whatever...) does not provide is any additional runway capacity. Therefore it's not really addressing the SE capacity problem.
It is intended to be a very high speed, mainly underground, new rail link basically following the route of the M25. 15 minute transit time. It is not intended to use any existing rail lines. But I can't see it happening. If something like this had already been implemented by far-seeing transport policy, say at the same time as the M25 was built or expanded, it would be a great inter-airport transfer link. But starting from scratch now - no way. Tunnelling is very very expensive.