As a Scot, I am skeptical how HS2 is going to improve the Edinburgh and Glasgow lines to London. Considering they don't go via Birmingham (they go Warrington, Stoke, Milton Keynes)
The west coast HS2 route threads between Birmingham and the existing West Coast Main Line, with a branch to Birmingham and a branch to join up with the WCML at (IIRC) around Crewe. It's a little less direct than the existing route, but engineered a lot faster.
The other dirty not-quite-secret about HS2 is that it's not mainly about high speed. The WCML is full to bursting in some sections, and putting freight, long distance passenger, and stopping trains on the same tracks reduces capacity further. So it's mostly about building a new line. And once you're doing that, it makes sense to make it high speed and passenger only.
