Donald Trump respects Boris Johnson for “calling it as he sees it”, the US ambassador to the UK has said, responding to the new prime minister’s 2015 description of the US president as “frankly unfit to hold office”.

Woody Johnson said the relationship between the two would be “sensational”. “I think they do have a lot [in common],” he said. “Both these leaders have their own style, but they have similarities and I think they have clear vision of what they want to accomplish.”

Speaking following the new prime minister’s election as Conservative party leader on Tuesday, the president heaped praise on Johnson, describing him as “Britain Trump”.

“We have a really good man who’s going to be the prime minister of the UK now,” Trump said. “He’s tough and he’s smart. They’re saying ‘Britain Trump’. They call him ‘Britain Trump’ and people are saying that’s a good thing.”

In an interview on BBC Radio 4’s Today programme on Friday morning, the US ambassador was asked if Trump was aware of critical comments Johnson had made about the president when he was mayor of London in 2015.

Responding to Trump’s claim that there were “no-go areas” in London where police feared for their lives, Boris Johnson said the then presidential candidate was “betraying a quite stupefying ignorance that makes him frankly unfit to hold the office of president of the United States”.

Woody Johnson said he was sure the president was aware of the comments. “Donald Trump is going to say what he wants to say when he wants to say it and he will comment on injustices or inabilities or how he sees it,” he said. “I think he respects Boris for the same. Boris is going to call it as he sees it.”

“But first of all I don’t think it’s long-lasting and second of all I think they have so much more in common in terms of what they want to accomplish for the good of both of our nations.”

He added: “The UK is our most important ally, both in security and also in prosperity, so you’re very important and he knows that, and he’s made some comments regarding a free trade agreement and putting the UK at the front of the line.”

The ambassador was asked about the resignation of the former UK ambassador to the US, Kim Darroch, following the leak of confidential cables in which he described a dysfunctional White House under Trump. “Leaks are devastating, as we have seen. Having known Sir Kim I wish him well going forward,” said Johnson.

The comments come as the prime minister heads to the West Midlands with the home secretary, Priti Patel, to promote his plan to recruit 20,000 police officers. Kit Malthouse, who was appointed policing minister on Thursday, told BBC Radio 4’s Today programme that the plans were ambitious, “in the nature of the new prime minister”.

Malthouse said the government would have to “sit down and look at the logistics” when asked whether they would have to reopen some of the more than 600 police stations closed since 2010 in order to accommodate the new recruits.

On Thursday night, the high-profile Eurosceptic Steve Baker said he had rejected a job on Boris Johnson’s frontbench because he did not want to repeat the “powerlessness” he felt as a junior minister before he quit over objections to Theresa May’s deal.

It is thought that the prime minister was hoping to keep Baker, who is the vice-chair of the hard-Brexit European Research Group, “inside the tent” as one of the key leaders of rebel Brexiters in parliament.

“Steve has said that he has full confidence in the prime minister to get us out of the EU on 31 October in line with the promises he’s given,” said Malthouse “There is a big job for us to do that over the next few months.”