So cancel it, and Crossrail, and put the money INTO the existing rail budget. It really doesn't get simpler!
As explained earlier, that's not how transport expenditure works. Cancelling one scheme does not mean the money is made available for another.
There are many people very vocal about the seeming disparities about rail spending in the South. The fact of the matter is many northern cities and actually depopulating: Liverpool, Hull, Middlesbrough are examples. Rail demand is lower because people's work patterns are different, often driven by house prices. Although there are people commuting into Manchester, Leeds, Glasgow and Edinburgh and many improvements have been proposed.
Work in the North tends to be low paid retail and call-centre work (with some exceptions) and houses are affordable. This is rather than high value, high skill jobs that exist in the SE, parts of the south and Midlands, with much of the population locked out of the housing market.
With London's population due to rise by several million over the next few decades, and house prices climbing, transport capacity has to be met somehow, hence Crossrail.
I support HS2 because I would like to see more high value jobs shifted toward the post industrial northern cities, and that's only going to happen with fast transport improvements and associated agglomeration.
Some of the critics claims are laughable, some are sensible.
Many of the claims that are made do not reflect the real world situation: For example one common claim is it will be a white elephant, when we know that N-S rail demand is growing at such a rate it could double in a decade. People are attracted to faster journey times, and time savings are important to the economy. It's the difference between taking a job and not taking a job, of busines being developed in an area, and the overall quality of life.
Another claim is there is no environmental case. While it's true that if you don't take into account the freight and commuter paths that are freed up on classic route, it's roughly carbon neutral (again assuming current power supplies) that certainly isn't the case with the alternatives. Indeed, people should be careful above making such claims about we shouldn't be doing X because it has some effect, because the reality is almost all human development has environmental effects and paradoxically the people that live in the Chilterns tend to have some of the largest carbon footprints in the land, and use the most resources. It's not that we should concrete over the countryside, but I'm confident that a well engineered railway through the countryside is more preferable than a motorway or large airport, especially when the former will probably be behind sound barriers or in tunnels passing through sensitive areas.