I don't entirely understand the plan. It seems to be a case of drawing a straight line across a map, ignoring possible gradients and hoping to get planning permission.
I also don't understand why there's no plan to connect it with HS1. Birmingham or points north to Paris/Lille should be a no-brainer, surely?
Hm? Do you mean the straight line in the Channel 4 article? But you'll find the detailed route maps here. It's very detailed, they even bothered with vertical curvature radius. You also find the different route options studied in chapters 5-7 of the report.
no plan to connect it with HS1
It's in the above linked part of the report, Chapter 9. Three options are investigated. It ends with:
The capital cost of the options for connecting to HS1 are presented below. Option 1 = £457,730,400 Option 2 = £812,165,920 Option 3 = £3,595,290,000
