Not a chance. A referendum is a very blunt tool to deal with often very nuanced issues. You’d have two main issues in this case. Firstly, I’d expect a very low turnout as most people (especially those in unaffected parts of the country) simply won’t care, they will have no reason to go out and vote for it. Secondly, the ‘no’ camp can easily mount a campaign around the theme of ‘spend the money on [insert cause] instead’ which will hit voters on an emotional level and will be virtually impossible to counter.
Major infrastructure project are incredibly expensive and often have a whole heap of vested interests. Decisions need to be made by politicians with a long term vision and the courage to see it through - sadly, these no longer seem to exist on any side. As a result, we will just keep muddling through and messing up while the rest of the world moves forward. HS2 Will join Heathrow expansion as a project that’s a no brainier in terms of the benefits, but politicians don’t have the guts to see it through.