Donald Trump will land in the UK on Monday amid anger over comments made by his ambassador suggesting the NHS should be “on the table” in future trade negotiations.

His visit also came as cabinet ministers vying for the Tory leadership suggested they could tear up plans for the Chinese tech giant Huawei to build parts of the UK’s 5G network, after the ambassador, Woody Johnson, warned it was “a big risk”.

Trump, who will meet the Queen at Buckingham Palace on the first day of his state visit, will be met by thousands of protesters in London the following day during a visit packed with pomp, pageantry and controversy that has seen numerous calls for its cancellation.

Johnson stoked opposition on Sunday after suggesting the UK would need to allow US agricultural products, including chlorinated chicken, on to the UK market as part of any post-Brexit trade deal, as well as US private sector involvement in the NHS.

The administration is said to see the visit as an opportunity for a “reset moment” on trade, with Theresa May set to formally resign on Friday.

Addressing the prospect of a transatlantic trade deal, Trump told reporters before leaving the US: “(We’re) going to the UK. I think it’ll be very important. It certainly will be very interesting. There’s a lot going on in the UK. And I’m sure it’s going to work out very well for them.

“As you know, they want to do trade with the United States, and I think there’s an opportunity for a very big trade deal at some point in the near future. And we’ll see how that works out.”

May called the visit “a significant week for the special relationship and an opportunity to further strengthen our already close partnership”. She stressed the need to build closer trading ties.

“We are the largest investors in each other’s economies and our strong trading relationship and close business links create jobs, opportunities and wealth for our citizens,” she said, adding that the government was looking forward to “building on the strong and enduring ties between our countries”.

Trump, who has endorsed the Tory leadership frontrunner Boris Johnson, had been a vocal critic of the prime minister’s proposed Brexit deal, which would have kept a customs arrangement with the EU for free movement of goods, which the US believed would scupper any comprehensive deal.

Woody Johnson, US ambassador: ‘I think the entire economy, in a trade deal, all things that are traded would be on the table.’ Photograph: HANDOUT/Reuters

The health secretary, Matt Hancock, became the first leadership contender to explicitly rule out any trade deal that put the NHS on the table.

“I love our NHS – it’s been there for me and my family when we have needed it most, and I want to make sure it is always there for all families,” he said ahead of the president’s arrival. “So I have a clear message: the NHS is not for sale and it will not be on the table in any future trade talks.”

The US ambassador, who is a close friend of the US president, said every area of the UK economy would be up for discussion when the two sides brokered a trade deal.

Asked if the NHS was likely to form part of trade negotiations, he told the BBC’s Andrew Marr Show: “I think the entire economy, in a trade deal, all things that are traded would be on the table.” Asked if that specifically meant healthcare, he said: “I would think so.”

His comments prompted an alarmed reaction from opposition politicians. The shadow health secretary, Jon Ashworth, said the comments were deeply concerning.

“The ambassador’s comments are terrifying and show that a real consequence of a no-deal Brexit, followed by a trade deal with Trump, will be our NHS up for sale. This absolutely should not be on the table,” he said. “Nigel Farage and the Tories want to rip apart our publicly-funded and provided NHS. Labour will always defend it.”

Johnson was also pressed on whether the US would seek a loosening of agricultural standards, including the importation of chlorinated chicken. He said the products should be offered to British consumers who could decide whether to buy them.

“There will have to be some deal where you give the British people a choice,” he said. “American products can come over … but if the British people like it, they can buy it; if they don’t like it, they don’t have to buy it.”

In his Sunday interview, the US ambassador also issued a veiled warning to May’s successor over the involvement of Huawei in UK infrastructure, saying he would “caution” the British government not to make any rushed decisions.

The highly controversial decision is reported to have been given the go-ahead after a tense national security meeting where May had the casting vote to allow Huawei to build “non-core” parts of the network, despite cabinet opposition. The defence secretary Gavin Williamson was sacked for leaking details of the meeting.

Speaking to CBS, the foreign secretary, Jeremy Hunt, underlined the growing UK government doubts about Huawei being given access to UK 5G networks.

He said that China “have said they want to have an 80% market share of telecoms technology and in other areas like artificial intelligence, they want a 90% market share by 2025 … And we have to ask as western countries whether it’s wise to allow one country to have such a commanding monopoly in the technologies that we’re all of us going to be depending on.”

He added that the UK would “never take a decision that affected our intelligence-sharing capability with the United States”.

Sajid Javid, who is also running to be Tory leader, said he would oppose Huawei’s involvement in the network. “I would not want any company, whatever country it is from, that has this high degree of control by a foreign government, to have access to our very sensitive telecommunications network,” he said.

Other topics likely to be on the president’s agenda will include the Middle East peace plan, set out in meetings with British officials by Jared Kushner, Trump’s son-in-law and architect of the so-called “deal of the century”, though the UK is likely to warn the plan needs more emphasis on political rights for Palestinians.

The Trump team are also likely to probe Downing Street to see if, once outside the EU, the UK might support US economic sanctions to force Tehran to reopen the nuclear deal. The US has hopes that a Boris Johnson premiership might back Trump’s approach.

The Donald Trump baby blimp will fly again. Photograph: Matt Dunham/AP

Trump will be accompanied by his wife Melania and his four adult children for the three-day visit. He will attend a state banquet at Buckingham Palace with May and the Queen on Monday. The Labour leader, Jeremy Corbyn,, the Commons Speaker, John Bercow, and the Lib Dem leader, Sir Vince Cable, have declined invitations to attend.

Trump is expected to meet May for formal talks in Downing Street on Tuesday and on Wednesday will travel to Portsmouth for the 75th anniversary of the D-day landings at Southsea Common, alongside over 300 D-day veterans and other world leaders.

The Stop Trump coalition said it was expecting huge crowds at its demonstration on Tuesday, after an estimated 250,000 people protested during Trump’s last visit. A giant inflatable Trump baby blimp, last seen when it was flown at his previous trip in June 2018, will fly again on Tuesday.

The protests have been backed by a senior Church of England bishop, who suggested Christian followers of Trump in the US were misinterpreting the faith. Paul Bayes, the bishop of Liverpool, said Trump’s populist way of doing politics was “toxic and dangerous”.

He said: “I don’t agree with him, I think he’s mistaken in many of his policies, and I think that the Christians who identify with him, especially in the US, are not properly responding to what our Christian faith says they should do.”