Donald Trump’s deteriorating relationship with Britain is likely to kill off any lingering cabinet hopes of a swift post-Brexit trade deal with the United States, a former British ambassador to Washington has warned.

Sir Nigel Sheinwald said that a series of controversial interventions by the US president in British issues meant that the remote prospect of a quick transatlantic deal, heralded by pro-Brexit cabinet members, should now be “put out of our minds” for good.

His intervention comes as a new poll highlights the British public’s opposition to Trump in the wake of his decision to cancel a trip to the UK, with fewer than a fifth of voters (18%) believing he is a friend of Britain.

Almost three-quarters of voters (72%) also believe that the US president is a risk to international stability, according to a new Opinium poll for the Observer. A similar proportion (71%) believe he is untrustworthy. Two in five voters believe that Trump should not be visiting Britain at all.

Sir Nigel Sheinwald, the former British ambassador to the US. Photograph: Paul Morigi/Getty Images

The dim view taken by the British public over the outspoken president comes after Whitehall insiders suggested that the clashes he has had with Britain over the last year contributed to his decision to cancel a visit to open the new US embassy in London. A mass protest had also been expected during Trump’s visit, which would have marked a further embarrassment for the president.

The special relationship between the UK and US has taken a series of hits since Theresa May became the first foreign leader to visit President Trump at the start of last year. Trump has attacked the London mayor, Sadiq Khan, re-tweeted posts by a British far-right group, and publicly turned on May for criticising his comments.

Trump confirmed on Twitter last week that he had cancelled a trip to open the new US embassy in Vauxhall because he disagreed with the process of moving it from Mayfair to an “off location” south of the Thames. While he blamed the Obama administration, the deal was signed under George W Bush’s presidency. In an extraordinary intervention, the US embassy itself took the step of releasing a detailed statement correcting the president. The highly unusual move is a sign of the tensions between Trump and his international diplomats.

Sheinwald, the British ambassador to the US from 2007 to 2012, said he had always believed that a swift trade deal with the US was unlikely, but that the latest episode should end hopes by some Brexiters that it could be done by Brexit day in March 2019.

“Given that Trump’s attitude to the UK seems to have changed for the worst over the last year, at least in a superficial and tonal way, I think that takes out another of the arguments for thinking that this would be a great positive for the UK in the post-Brexit world,” he said. “It will be important for us to get a deal with the Americans, but it will take a long time.

“If you’re a Liam Fox [the international trade secretary], who has staked so much on the American deal being easy and within our reach around the same time as Brexit, then the way in which the bilateral relationship has atrophied and the tone has changed in the last year since May’s first visit is quite a big blow.

“It means we should put out of our minds the idea that just around the corner when we leave the EU there is a magical deal with the US that is going to solve all our trade and industrial problems. Absolutely not.”

Sir Christopher Meyer, another former British ambassador to the US, said that he believed the current cooling of relations made little difference, as the chances of a swift deal had always been far-fetched.

Sadiq Khan, who welcomed Trump’s decision to shelve his trip to the UK, was targeted by pro-Trump protesters yesterday as he gave a speech in central London. His address was delayed by a few minutes after a demonstration by a group called the White Pendragons. They were escorted out of the venue by police.

After Trump’s recent declaration that he believed he was a “stable genius”, many British voters compare themselves favourably against the president’s intellect. Almost half (47%) believe they are more intelligent than Trump, according to the Opinium poll. More than two-fifths (44%) believe Trump is less intelligent than the average person. A fifth (18%) believe he is more intelligent than average.

In terms of overall party support, the poll showed that Labour and the Tories are now neck-and-neck on 40% support. It means Labour has relinquished a two-point lead from a month ago. The Liberal Democrats continue to struggle on just 6% support. Vince Cable, the Lib Dem leader, has a lower net approval rating (-19%) than either Jeremy Corbyn (-10) or Theresa May (-17%).

May’s lead over Corbyn on who would make the best prime minister has fallen very slightly, from six points to five points.