The face said it all. As Rachel Reeves listed the infrastructure projects being funded by her first budget, she could not even say how much the biggest one would cost. She announced a £22.6bn cash injection for the NHS in England over two years and an extra £2.3bn a year in core funding for English schools. Television showed the relevant ministers cheering to the skies. But when she mentioned a certain railway tunnel from Old Oak Common to Euston in London, the transport secretary, Louise Haigh, was not cheering. We saw only a jaw tightening into what looked like a grimace.

HS2, the greatest white elephant in British history, has lived to fight another day. Once costed at £30bn and then soaring to £100bn, even stripped of its northern limbs it is currently expected to cost £67bn. A year ago Rishi Sunak added himself to the list of shame of prime ministers who lacked the courage to kill it. But he did stop the building of the London link from Old Oak Common to Euston. The cost of the Euston terminus alone had ballooned from £2.6bn to £4.8bn. It was clearly out of control and the London end of the project was in effect banned.

Winding up the work and securing the site was expected to cost a mind-blowing £200m. Two giant tunnelling machines now sit buried under Old Oak Common. Around them spread acres of desolation – of evicted families and flattened businesses. But at least it half made sense. Sunak could then redistribute the alleged £6.5bn it would have cost to finish the project to urgently needed rail projects in the north.

The only future Sunak could offer for Euston was that a private developer might step forward to pay for the tunnel and the new station out of the profits from the rest of the site. Since this seemed improbable, the assumption was that sooner or later, a government might have the wit to admit that it was all a ghastly mistake and return the Euston acres to the people of Camden.

Last February the Commons’ public accounts committee reviewed Sunak’s decision on Euston. Its report made dire reading. It in effect dismissed the entire HS2 project as “very poor value for money”. But it particularly remarked that his privatisation of Euston did not add up. Whitehall did not have “a plausible or detailed proposition it could take to the market”, the committee said, and was “likely to take significant time to develop one”.

The former chief economist at Arup, Alexander Jan, has calculated that little more than £500,000 in annual revenue could be recouped from a Euston development. To pay for even a modest tunnel and station at, say, £4bn would involve building the equivalent of 21 Canary Wharf towers plus 80,000 homes. Jan concludes that this would be “absurd”. To get even a fraction of the needed revenue, an obscene wall of offices and luxury flats would need to rise over Regent’s Park and Bloomsbury, obliterating the view of the City and St Paul’s from Primrose Hill. For this to have emanated from Downing Street is the measure of how hard it is to take modern British government seriously.

Continuing the tunnel to Euston, at an estimated cost of £1bn, makes sense only if Reeves is going to return something like Sunak’s £6.5bn to Euston. This is a huge sum – more than twice the £3.1bn increase over two years in the NHS’s capital budget announced this week. It will have to come either from other announced rail projects in the north – money promised by Sunak – or from elsewhere in her budget. In other words, it is either Primrose Hill or Manchester-to-Leeds and eat your heart out, levelling up.

The rump HS2 to Birmingham has never been under serious budgetary control. We never get the full figures, and a recent BBC Panorama report included a claim that some of those presented by HS2 to government were deliberately misleading. The transport department has always treated HS2 as too big to fail. And a measure of the project’s political clout is that Keir Starmer’s rail minister, responsible for HS2, is Lord Hendy, a rare HS2 champion as the former chair of Network Rail. Meanwhile HS2’s virtues are presumably to be vetted by the new Office of Value for Money, chaired by none other than David Goldstone, who just happens to act as a non-executive director of HS2 Ltd as the Treasury’s representative on the board. The whole affair is pure banana republic.

At every critical stage in HS2’s development, the sensible policy would have been to call a halt to what was David Cameron’s silliest vanity project. The money could have been spent on a dozen transport projects more needed than knocking half an hour off a trip from London to Birmingham. Easing capacity at Waterloo and Paddington would make more sense than at Euston, as would improving the north’s diabolical rail links.

It would still be worthwhile to cancel HS2. Twelve years of planning has made not an ounce of difference to its poor value for money. Even Sunak’s terminus at Old Oak Common would be reasonable. Haigh’s claim that it would make “absolutely no sense” to abandon Euston is like saying that every white elephant needs a tail.

Old Oak Common will connect with London’s new transit spine, the Elizabeth line, which Euston does not. More to the point, nearby Acton’s derelict industrial acres are to become the Canary Wharf of the western metropolis, one of Europe’s most dynamic “new towns”. To link the Midlands to Acton rather than the British Museum and London zoo will one day seem perfectly reasonable. As it is, Britain’s infrastructure planning seems as incompetent as ever.

• Simon Jenkins is a Guardian columnist