The strategists at the heart of the campaign to leave the European Union were in no doubt about what won it for them. “Would we have won without £350m [for] NHS?” said Vote Leave campaign director Dominic Cummings. “All our research and the close result strongly suggests no.” Insiders knew that, without that big red bus promising £350m more a week for health services, the British voters would not have given them their narrow victory.

That is why it is so maddening that this pledge has turned out to be a simple lie. Yesterday, the official Treasury figures for UK contributions to the EU budget came out. In 2016/17, it showed, the UK contribution to the budget was just £156m a week – less than half of what Vote Leave promised. The entire Vote Leave campaign was built on 200 million little lies.

This, of course, was perfectly apparent during the referendum campaign. Andrew Dilnot, the head of the impeccably impartial UK Statistics Authority, called the £350m figure “potentially misleading”. The figure was savaged by the then chair of the House of Commons Treasury Select Committee, Andrew Tyrie. A Conservative MP himself, he called it a “false prospectus” that amounted to “nonsense politics” and “a form of electoral bribery.” But seeing the lie busted in black and white on a balance sheet proves conclusively how utterly misleading it was.

The tragic truth is that Brexit, and especially the hard Brexit course this Government is charting, will mean less money for our NHS rather than more. The government’s own forecasters, the Office for Budget Responsibility, have forecast that Brexit will be directly responsible for a £58bn black hole in the public finances. This can only be filled by raising taxes or cutting spending – for example, on the NHS. I think we all know what choice this Tory government would make in that scenario. The independent Institute for Fiscal Studies has likewise concluded that the government’s decision to leave the single market alone will weaken the public finances by £8bn in 2019-20. To minimise the damage of Brexit to our NHS, the government should be negotiating to keep Britain in the single market, as the Open Britain group is campaigning for.

Brexit is having another dire impact on our NHS – staff shortages. Our health and social care system is dependent on workers from the EU, with more than 60,000 of them working in our NHS alone. Since the referendum, there has been a shocking 96 per cent fall in the number of EU nurses applying to work in the National Health Service – and this is before we even leave the EU and the government institutes a more draconian immigration system. The Tories’ target of cutting annual net migration to the "tens of thousands" will clearly damage our NHS; even their leader in Scotland, Ruth Davidson, is now calling on them to scrap it.

The cynical right-wingers who ran Vote Leave won partly by misleading the British people on the consequences of Brexit for our NHS. They are already being found out. Given that those who voted for Brexit did so in part to boost health funding, ministers have an absolute responsibility to ensure that Brexit does not damage our NHS. They should start by welcoming rather than repelling EU nationals seeking to work here, and by negotiating to retain our place in the single market.

Chuka Umunna is a leading supporter of Open Britain