HS1 never announced any budget for any contract, so lots of bids came in way under what the government was prepared to spend, hence came in well under budget.
I seem to recall that was also due to infrastructure 'transparency' and government 'openness' from the 00s.
It got off to a bad start under Andrew Adonis in the dying days of the Blair/Brown administration, but people forget that.
"Adonis himself is openly regretful. “HS2 should stop at Old Oak Common,” he told me, “interchanging with Crossrail there. We should leave open the question of going further into London.” As head of the Cameron’s national infrastructure commission, Adonis makes many speeches on these subjects. He nowadays lauds HS3, and lauds Old Oak Common as London’s greatest development opportunity. I have yet to hear him laud Euston. That station, he says, “is the poison at the heart of HS2. I bitterly regret not stopping it before I left office”."
https://www.theguardian.com/uk-news/2016/jun/07/hs2-the-zomb...
https://www.independent.co.uk/news/uk/politics/hs2-rishi-sun...
> Mr Holden also said HS1 was successful because the true budget was known to just “a handful of people”, while HS2 contractors inflated their prices once they saw the latter project’s true budget.