If you take a look at the construction costs, of the $6.6Bn only £665 are going towards the rail and control systems. With all other items being largely the same regardless of rail speed, I have a feeling (though I could be quite wrong), that the cost difference between low and high speed is marginal.
Source: https://assets.publishing.service.gov.uk/government/uploads/...
We need some solid stats by an independent party which is why I'm happy one is going to be looking into it.
FYI from that document, let me quote cos it's interesting: cost estimates in march 2012:
2.9 Route package cost summaries
2.9.1 The phase one total cost estimate is £16.3 billion within a cost range of £15.4 billion to £17.3 billion. [...]
2.9.2 The phase two total cost estimate is £17.1 billion within a cost range of £15.7 billion to £18.7 billion. [...]
2.9.3 The full Y network cost estimate is £33.4 billion within a cost range of £30.9 billion to £36.0 billion. [...]
That has to happen whether the trains run at 180mph or 80mph.
However to be sure I'm not being unreasonabe I want to know what that curve is - am I being unreasonable to ask for information given that I'm going to be paying for HS2?