Here is an excellent explanation of the case for HS2. The interesting point made is that the Great Central alignment has a maximum top speed of 110 mph without tilt. But the speaker does not explain whether the whole route is so curvy that it would be limited to 110 mph throughout, or, if there are a few points which are speed-limited, and which could be straightened or by-passed, which would be an obvious thing to do if the route is reinstated. The East Coast Main Line used to have sharp curves at Offord and Selby, but the former was straightened by realignment and the latter by constructing a cut-off route.
The speaker also refers to the need to separate slow and fast trains. However,
The West Coast Main Line is four track all the way from London to Crewe, apart from the short section between Roade and Rugby, where the slow lines are routed through Northampton.
The East Coast Main Line is four tracks from London to Peterborough, apart from the Welwyn Garden City bottleneck.
The Midland Main Line, which could potentially run all the way to Manchester, used to have two additional tracks for slow train, all the way from London to Trent Junction, near Nottingham.
The speaker does not explain why a lower operating speed has not been chosen; the cost of building, equipping and operating a railway rises disproportionally once speeds rise above 100 mph. In the UK context, the optimum speed is probably between 125 mph and 140 mph.
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