Right then, needs a bit of flesh,
but here's a start. Using a bit of Chinese-level ambition I feel...
The network would be built, a bit like LE Greys, to a much larger gauge. I'd use a 2.25m track gauge. Loading gauge would allow stock to 6.5m high (easily allowing doublestack), and as wide as Eurotunnel shuttle.
The network shown in the image would be a 400km/h max passenger network. I'd flesh it out with a 200km/h secondary network, with 100km/h Metro and Rural routes. All 25kV overhead. The 400 network would be shadowed by 200 lines for services to intermediate towns and for freight. The two wouldn't always be on the same alignment, and freight would also gain "avoiding" routes round towns, serving major out-of-town industrial parks.
Note lines such as the London orbital and Welsh North-South. Routes are obviously just rough.
You said start from scratch...
Tunnels, Viaducts as needed and to hell with the NIMBYs.
Possible extension to Holyhead for a tunnel to Dublin.
Four more bores for the Channel Tunnel- to have a dedicated pair each for Shuttle, Freight and Passenger.