The trouble is HS2 is simply not ambitious enough. 240mph or whatever is simply not fast enough.
In Japan half of modern new lines are put underground, why not simply go the whole hog and put the whole beast in a tunnel? If you don't go to deep the build will be in soft rock/subsoil rather than hard rock. At is peak the Channel Tunnel was dug at half a kilometere a week and the record is 700m.
In other words London to Birmingham in 340 weeks, with a single boring machine. Now have at least four headings with faces located one quarter and tree-quarters along the route and that becomes a dig time of less than 2 years.
Make sure the line follows existing road/rail infrastructure but is straightened up. Put a maglev track in each tunnel, lightly vacuum it. Bit of innovation needed there, but not impossible. Put air out of the tunnel and the 1000mph railway is a possiblity.
London to Birmingham in 10 minutes. Every developed country in the world will be knocking at the door for the technology.
It can work here, because our transport needs are for short distance links with very intense usage.
Let's see the vision!