Steve Bannon, the far-right former adviser to US president Donald Trump, has said he offered advice to Boris Johnson in the run-up to his resignation as foreign secretary last summer.

Mr Bannon, who helped propel Mr Trump into the White House, said that he offered advice by text message ahead of Mr Johnson’s resignation speech in the House of Commons in July 2018.

The former London mayor used that speech to rip apart prime minister Theresa May’s Brexit strategy, accusing her of “dithering” and of leaving the UK in a “miserable limbo” amid a “needless fog of self-doubt”.

A spokesman for Mr Johnson, who is the frontrunner to become the next British prime minister, rejected Mr Bannon’s claims — saying that while the two men did exchange text messages that weekend they had been about the logistics of a potential meeting that never took place.

The spokesman said the two men had not met or spoken since that exchange.

Last year Mr Johnson dismissed any association with Mr Bannon, calling the theory a “lefty delusion whose spores continue to breed in the Twittersphere”. Instead, he said he had met Mr Bannon in his role as foreign secretary.

But that assertion appears to have been undermined by unused footage from a documentary by Alison Klayman, an American film-maker who followed Mr Bannon for a film called The Brink.

The Klayman clip, obtained by The Observer newspaper, shows Mr Bannon reading a Daily Telegraph article about Mr Johnson’s resignation speech.

“Today we are going to see if Boris Johnson tries to overthrow the British government. He’s going to give a speech in the Commons,” Mr Bannon told the director. “I’ve been talking to him all weekend about this speech. We went back and forth over the text.”

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Mr Bannon said he had got to know Mr Johnson during the transition period after Mr Trump’s election victory. He had been urging the foreign secretary to give a repeat of his “important” speech in the final hours of the Leave campaign in June 2016.

“And all I was telling him all weekend was just to incorporate those themes. Those same themes. Basically, he was saying that June 23 was independence day for Great Britain. Their independence day being like our July 4.”

On Sunday a spokesman said it would be reasonable for a foreign secretary and a chief of staff to the US president to communicate. However, the text messages occurred nearly a year after Mr Bannon had quit the White House in August 2017.

The spokesman added: “Steve Bannon did text Boris Johnson when he visited last summer to request a meeting, but the texts are along the lines of ‘can we meet up?’ and ‘will you be around?’ . . . Boris Johnson was unavailable and wasn’t around.”

Opinion polls over the weekend showed a slight shift towards his rival for the Tory party leadership, foreign secretary Jeremy Hunt, but Mr Johnson still appears to be the clear favourite among Conservative members.

A poll by Opinium on Sunday suggested that Tory members believed Mr Johnson was more competent and able to take big decisions than Mr Hunt. The survey found 57 per cent preferred Mr Johnson to negotiate Brexit against just 26 per cent for Mr Hunt.

A poll for ComRes found 61 per cent of Tory councillors intended to back Mr Johnson against 39 per cent for his rival.

But a third poll, by Survation, suggested Mr Hunt’s lead among Tory voters had fallen from 27 points to 11, with Mr Hunt ahead by three points among the general public.

At Saturday’s hustings for the Conservative party leadership Mr Johnson refused to answer questions about why police had been called to the flat Mr Johnson shares with his partner Carrie Symonds after a loud altercation in the early hours of Friday morning.

Liam Fox, the trade secretary — who is a Hunt supporter — on Sunday told the BBC’s The Andrew Marr Show that Mr Johnson should answer the question. “It’s always easier to give an explanation, then we can discuss the policies, he said.”