Whether Conservatives can be trusted with the NHS is an old question at election time. Whether Boris Johnson can be trusted on anything is an issue for the current campaign. The two questions make a dangerous combination for the Tory leader, who is expecting the country to believe that he would protect the health service in a post-Brexit trade deal with Donald Trump.

There is not much reason to believe that he would. On Wednesday Labour sought to probe that concern, revealing documents containing a full account of preliminary discussions between US and UK officials.

Jeremy Corbyn declared this to be proof that the NHS is “up for sale”. There is some campaign hyperbole in that assertion. The leak shows that the US is interested in the UK healthcare market and that discussions had covered patent lengths, which affect the profits of American pharmaceutical companies. It is no secret that the US resents the leverage available to the NHS as a large state-owned consumer of medicines. Washington would see breaking that monopoly as a core objective of trade talks, inflating prices. Dismantling state provision so private insurance companies can expand in the British market would also be a desirable outcome for US lobbies, but not for British citizens.

Mr Johnson has insisted many times that the NHS is not vulnerable to US corporate aggressions, including in a recent televised debate with Mr Corbyn. Labour says the leaked documents destroy the prime minister’s defence, although that did not stop him repeating it on Wednesday. Both sides have a technical truth on their side. The NHS is formally “on the table” in talks because the Americans have put it there. But the UK government has not yet acquiesced to any demands. Formal negotiation is not yet at ministerial level. Mr Johnson can continue to claim that he would never yield, but a long record of dishonesty makes his pledges worthless. He is already associated with one of the most conspicuous falsehoods of recent British political history – the referendum campaign claim, printed on the side of a bus, that £350m a week could be diverted from EU budgets to the NHS. The current Tory manifesto includes a duplicitous claim to employ 50,000 more nurses, 18,500 of whom would in fact be existing nurses retained in post.

Even if Mr Johnson was a more reliable figure, his handling of Brexit makes a nonsense of any claim that he might stand up to Washington. Talks with Brussels clearly demonstrated the imbalance of power between the UK and a continental trading bloc. Mr Johnson’s deal, combined with a manifesto pledge not to extend transitional terms, sends the UK hurtling towards a very hard Brexit by the end of 2020. The Tory party would be desperate to show progress towards a US deal to compensate for the loss of access to European markets. A diminished Britain, having relegated itself from the top tier of trading powers, would find itself taking dictation from American negotiators enforcing President Trump’s demands. The leaked documents contain a revealing foretaste of what that would involve: US insistence that climate change and carbon emissions form no part of any future agreement; expectation of access for US agribusiness and its notorious chlorine-washed chicken. Officials even offered their British counterparts advice on how to sell the unpalatable idea to sceptical domestic audiences.

What Mr Johnson says on these matters now is no guide to what he would do. It has long been obvious that he will say whatever he finds expedient to get from one day to the next. Even if his statements of intent to protect the NHS coincide with actual beliefs – and it is unclear that he possesses any – he would be too weak to enforce the pledge. The Tory leader was wrong about “taking back control” in 2016. His Brexit deal surrenders control. US corporate interests would be the beneficiaries; the NHS would be their prey.

• This article was amended on 29 November 2019 to replace “new nurses” with “more nurses”, the phrasing used in the Conservative party’s manifesto.