Downing Street has insisted it will not comment on “speculation” following reports that Boris Johnson’s former aide, Dominic Cummings, is being blamed for leaking the Prime Minister’s text messages.

An internal inquiry has been launched into how messages between the Prime Minister and billionaire Sir James Dyson were leaked to journalists, amid an ongoing row over lobbying in Whitehall.

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

Repeatedly quizzed about the reports during a Westminster briefing, a No 10 spokesman told reporters: “We have instructed the Cabinet Office to look into the Dyson leak.

“I am not going to comment on speculation and, of course, it is for the Cabinet Office to take that work forward, I am not going to pre-empt it.”

The Times, Daily Telegraph and Sun all reported comments from an insider naming former aide Mr Cummings, who is yet to respond to the accusations.

“Dominic is engaged in systematic leaking,” a source told The Times.

“We are disappointed about that.

“We are concerned about messages from private WhatsApp groups which have very limited circulation.”

Labour leader Sir Keir Starmer criticised the “quarrelling” when asked about the reports during a campaign visit to Hartlepool.

“Now we’re getting arguments and quarrelling at the centre of government about who is leaking information about privileged access,” he told reporters.

“Boris Johnson is desperate to try to put this at arm’s length, but it’s obvious that he can’t. This is government by WhatsApp, they’re all at it.”

Mr Johnson promised Sir James he would “fix” a tax issue for Dyson staff working to develop ventilators at the height of the coronavirus crisis last year, in text messages obtained by the BBC.

The leak of the texts to the entrepreneur was not the first time the Prime Minister’s messages have been made public.

Mr Johnson was sent a text message by Saudi Crown Prince Mohammed bin Salman as a bid to buy Newcastle United FC ran into difficulties last June.

A No 10 source told The Sun that Mr Johnson “fears Dom was responsible for the text message leaks about James Dyson and Mohammed bin Salman”.

The former Vote Leave mastermind worked closely with Mr Johnson on the Brexit campaign and was a major figure in No 10 after the Prime Minister took office.

Mr Johnson stood by him after Mr Cummings found himself in the eye of a media storm after driving his family to County Durham during the coronavirus lockdown.

But Mr Cummings was subsequently ousted from Downing Street amid the fallout from an internal power struggle with the Prime Minister’s fiancee, Carrie Symonds.

No 10 had initially said there would not be a probe into how the exchange with Sir James was made public, but a change of course was announced on Thursday as it said an internal inquiry will be led by the Cabinet Office.

Mr Johnson told the Commons during Prime Minister’s Questions earlier this week that he was “happy to share all the details” of the exchanges as there is “nothing to conceal”.

“I make absolutely no apology at all for shifting heaven and earth and doing everything I possibly could, as I think any prime minister would in those circumstances, to secure ventilators for the people of this country,” he added.

The BBC reported that the messages between Mr Johnson and Sir James were exchanged in March last year after the businessman was unable to get the assurances he was seeking from the Treasury.

Sir James, who has changed his main address in business filings to the UK from Singapore, wrote to the Treasury requesting that his 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.