The main justification that has been given for HS2, apart from marginally reduced journey times, is that the West Coast Main Line will soon be full. When the WCML upgrade was first proposed, it included a version of ERTMS, which would have allowed trains to operate at higher speeds (140 mph) and headways to be shorter. This would have vastly increased capacity.
As an example, the new high speed line between Shanghai and Nanjing in China, which has CRTMS (the Chinese equivalent of ERTMS) working from day one, has trains departing as little as every three minutes, with line speeds of up to 380 km/hr.
As the WCML upgrade progressed (or rather didn't), it was soon realised that due to the absence of a proper diversionary route, to keep trains running and reduce cost over-runs, it would be necessary to de-scope and in-cab signalling was eliminated.
At some time in the future, it will be necessary to take this pain and introduce ERTMS on the WCML, so, to lessen this pain, increase capacity and avoid the need for a high speed line, here's a much lower cost solution: -
1. Electrify the Midland Mainline (looks like it might happen anyway);
2. Reinstate the 16 miles of missing main line railway between Matlock and Millers Dale Junction, enabling through trains to operate between Manchester and London via the Midland Mainline - this was a critical element of the original electrification of the WCML in the sixties, providing a credible diversionary route whilst the WCML was undergoing knitting. Peak Rail is of course an issue, but if they are granted running rights on summer Sundays and someone else is paying to maintain the infrastructure, they might actually be better off than they are now;
3. Equip the WCML with ERTMS, using the newly electrified and extended Midland Mainline, plus the Chiltern as diversionary routes to / from Birmingham, Manchester and all points North & West;
4. Forget HS2 for another fifteen years, until UK plc has got its books balanced and is living within its means.
I believe that this would offer much of the increased capacity that HS2 would provide at a fraction of the cost and the only sacrifice would be the marginally reduced journey times, which seem to be acceptable to most people as they are and would in any case be improved with 140 mph running.