Messages obtained by the BBC revealed Mr Johnson promised to ‘fix’ a tax issue for Dyson staff working to develop ventilators early on in the coronavirus crisis.

Reports on Friday said Downing Street sources were pointing the finger at Mr Cummings, who quit as the PM’s senior adviser last year following a behind-the-scenes power struggle in No 10.

In a post on his blog, Mr Cummings said: ‘I do have some WhatsApp messages between the PM/Dyson forwarded to me by the PM. I have not found the ones that were leaked to Laura Kuenssberg on my phone nor am I aware of being sent them last year.

‘I was not directly or indirectly a/the source for the BBC/Kuenssberg story on the PM/Dyson texts.’

Mr Cummings also claimed he warned Mr Johnson against plans to have donors secretly pay for refurbishment of his Downing Street flat, saying they were ‘unethical, foolish (and) possibly illegal’.

He said: ‘It is sad to see the PM and his office fall so far below the standards of competence and integrity the country deserves.’

Mr Cummings denied leaking the messages to the BBC

No 10 launched an internal inquiry led by the Cabinet Office into how messages between the Prime Minister and Sir James were leaked to the BBC.

A spokesman declined to deny suggestions the controversial former aide is the suspect when repeatedly questioned during a Westminster briefing with journalists.

Mr Cummings said he is ‘happy to meet with the Cabinet Secretary’ and to have his phone searched.

He added: ‘If the PM did send them to me, as he is claiming, then he will be able to show the Cabinet Secretary on his own phone when they were sent to me.

‘It will therefore be easy to establish at least if I was ever sent these messages. I am also happy to publish or give to the Cabinet Secretary the PM/Dyson messages that I do have, which concerned ventilators, bureaucracy and covid policy — not tax issues.’

The leaked text messages showed that in March last year Mr Johnson promised Sir James he would ‘fix’ a tax issue for Dyson staff working to develop ventilators.

At the time, the businessman had been unable to get the desired assurances he was seeking from the Treasury over his Singapore-headquartered firm.

Sir James wrote to the Treasury requesting that overseas staff would not have to pay additional tax if they came to the UK to work on the ventilator project.

But when he failed to receive a reply, Sir James reportedly took up the matter directly with the Prime Minister.

He said in a text that the firm was ready but that ‘sadly’ it seemed no-one wanted them to proceed, to which Mr Johnson replied: ‘I will fix it tomo! We need you. It looks fantastic.’

The Prime Minister then texted him again saying: ‘(Chancellor) Rishi (Sunak) says it is fixed!! We need you here.’

Two weeks later, Mr Sunak told the Commons Treasury Committee that the tax status of people who came to the UK to provide specific help during the pandemic would not be affected.

Sir James said he was ‘hugely proud’ of his firm’s response in ‘the midst of a national emergency’, and that he would ‘do the same again if asked’.

He told the BBC: ‘When the Prime Minister rang me to ask Dyson to urgently build ventilators, of course, I said yes.

‘Our ventilator cost Dyson £20 million, freely given to the national cause, and it is absurd to suggest that the urgent correspondence was anything other than seeking compliance with rules, as 450 Dyson people – in UK and Singapore – worked around the clock, seven days a week to build potentially life-saving equipment at a time of dire need.

‘Mercifully, they were not required as medical understanding of the virus evolved. Neither Weybourne (Dyson’s holding company) nor Dyson received any benefit from the project; indeed commercial projects were delayed, and Dyson voluntarily covered the £20 million of development costs.’

Sir James also said his company had not claimed ‘one penny’ from governments in any jurisdiction in relation to Covid.