Donald Trump has intervened in the UK’s nascent election campaign, calling on Boris Johnson to team up with Nigel Farage to form an “unstoppable force” and claiming Jeremy Corbyn would be “so bad for your country”.

Speaking to Farage on LBC Radio, the US president also said Johnson’s Brexit deal could prevent the UK from agreeing a trade deal with the US.

Trump said the US “can’t make a trade deal with the UK” under “certain aspects of the deal”, despite Johnson’s claims it would allow the UK to have an independent trade policy.

One of Labour’s main attacks against Johnson has been that the prime minister would be too close to Trump and allow a sell-off of public services to US companies as the price of a trade deal, with the NHS potentially on the line.

Trump told LBC listeners that he was not interested in buying the NHS, and criticised Corbyn as “so bad for your country”.

“He’d be so bad, he’d take you in such a bad way. He’d take you into such bad places,” he added.

Trump told Farage he had reservations over Johnson’s deal, because it could prevent trade with the US, but he denied Corbyn’s claims it would mean the NHS was up for sale to American health corporations.

“I don’t even know where [it] started with respect to us taking over your healthcare system. I mean it’s so ridiculous. I think Corbyn put that out there, but to even think, it was never even mentioned, I never even heard it until I went over to visit with the Queen,” he said.

Play Video Trump tells Farage that Corbyn would take UK to ‘such bad places’ – video

During that trip, Trump had fuelled speculation that the US would want access to NHS contracts for US corporations by saying that “everything is on the table”. He later backtracked by saying: “I don’t see [the NHS] being on the table.”

A No 10 spokesman contradicted Trump’s claim that a UK-US trade deal might not be possible under Johnson’s Brexit withdrawal agreement. “The PM negotiated a new deal which ensures that we take back control of our laws, trade, borders and money – a deal which people said he could never negotiate. Under this new deal the whole of the UK will leave the EU customs union, which means we can strike our own free trade deals.”

On Johnson, the US president said: “We want to do trade with the UK but to be honest with you, this deal, under certain aspects of the deal, you can’t do it. You can’t trade. We can’t make a trade deal with the UK. I think we can do many times the numbers we’re doing right now, and certainly much bigger numbers than you’re doing under the EU. Boris wants to be very careful with it. Under certain ways we would be precluded, which would be ridiculous.”

In remarks that are unlikely to be welcomed in Downing Street, Trump said Johnson was a “fantastic man and [the] exact right guy for the times”, and added that he could form an “unstoppable force” by pairing with Farage.

Trump also told Farage that Johnson “has a lot of respect and like for you”.

“He respects you a lot, I can tell you that, he respects you a lot, I don’t know if you know that or not,” Trump told Farage. “But, cause I have no idea I have enough to do over here without having to worry about the psychology of two brilliant people over there, frankly ... I wish you two guys could get together, I think it would be a great thing.”

Responding to the US president’s comments, Corbyn accused Trump of “trying to interfere in Britain’s election to get his friend Boris Johnson elected”.

“It was Trump who said in June the NHS is ‘on the table’. And he knows if Labour wins US corporations won’t get their hands on it. Our NHS is not for sale,” Corbyn tweeted.

Farage agreed with Trump’s criticism of Johnson’s deal, as he has been arguing that it represents “Brexit in name only”. He vowed the Brexit party would challenge the Conservatives at the ballot box.

However, Farage has refused to be drawn over reports the Brexit party is engulfed in a row over how many seats it should contest at the election. Some Brexit party supporters and candidates are concerned that the leave vote could split and boost Corbyn’s chances. Farage described the idea that his party may only focus on 20 to 30 leave-voting Labour seats in the north of England as “idle speculation”.

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At the Brexit party launch on Friday, Farage will reveal his strategy for the campaign after coming under pressure from two different factions in his party. On the one side, some pragmatists are warning that standing in Tory-Labour marginals could help Corbyn.

But many of his candidates are desperate to run and oppose Johnson’s deal, which they see as not being a “real” Brexit.

Farage, who has been at a Trump hotel in Washington DC this week, explained his party’s dilemma on a podcast alongside the former Trump aide Steve Bannon.

“Here’s the problem. We’ve got the forces of remain, the globalists. We’ve got the Liberal Democrats who want to literally cancel the results of the referendum. Labour, they want a second referendum. We’ve then got my position which is we leave the EU institutions and become an independent country.

“Boris Johnson, who is very jolly, brings a lot of energy and optimism and is a thousand times better than Theresa May, [but] he has basically picked up Mrs May’s failed deal. It is not a deal … Boris is trying to deliver Brexit in name only to an exhausted public ... it’s not great. If Boris signs this then my view is that we will not have a proper trade deal with the US.”

He also dismissed fears about food and medicine shortages during a no-deal Brexit, saying: “During the war, the German U-boats sunk a lot of ships and we still didn’t starve.”

Robert Hayward, a Tory peer and election analyst, said on Thursday that the Conservatives could actually suffer in some places if the Brexit party stood down its candidates.

“There is no certainty that the withdrawal of Brexit party candidates will automatically help the Tories,” he said. “In large swathes of the Midlands, north and Wales, Brexit voters are ex-Labour voters and would – to misuse a well known phrase – ‘rather die in a ditch’ than vote Tory. There are therefore many marginals in those areas where the presence of a Brexit candidate would help the Tories not hinder them.”

There was disaffection among some Brexit party candidates about the idea of drastically reducing the number of seats the party contested.

Ahmad Malik, the candidate for Chesham and Amersham, tweeted that the Brexit party was “NOT an appendage or facsimile of the Conservatives”, and added: “How can you ‘split’ a vote that doesn’t exist?” Malik urged leave supporters to “hold your nerve and resolve”.

His tweet was shared by other party candidates who would be expected to stand down if the party rolled back its election efforts, including Malcolm McLeod in Rochester and Strood, and even some based in leave-dominated Labour seats, such as Faye Clements in Middlesbrough.