Downing Street has announced an internal inquiry into the leak of private text messages between Boris Johnson and billionaire Sir James Dyson over the tax status of his employees.

Mr Johnson promised the entrepreneur he would “fix” the issue after personal lobbying from Sir James as he sought to build ventilators at the height of the coronavirus crisis, in a series of text messages seen by the BBC.

No 10 had initially said there would not be a probe into how the exchange 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.

The Prime Minister’s official spokesman told a Westminster briefing: “I can confirm that, yes, we have instructed the Cabinet Office to look into this.

“The position has changed from yesterday – it was correct at the time yesterday but, as usual, we keep things under review and we have now decided to undertake this internal inquiry.

“As you would expect, we continually look at this and the position we decided today is that we want to make sure we have this internal inquiry into that.”

The spokesman confirmed the inquiry will examine the source of leaks of Mr Johnson’s private communication “as related to this issue of Dyson”.

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Businessman Sir James Dyson contacted the Prime Minister directly (Jeff Overs/BBC/PA)

The BBC reported that a series of text 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.

Downing Street has said it will publish correspondence between Mr Johnson and Sir James “shortly”, after the Prime Minister told the Commons he was “happy to share all the details” of the exchanges.

The Prime Minister’s official spokesman said: “The Prime Minister said in the House he’s happy to share all the details with the House, as he shared them with his officials.

“That’s what we’re working on, we’re pulling together that information, it will be published shortly.”

Meanwhile, the spokesman did not deny reports that Cabinet Secretary Simon Case advised Mr Johnson to change his phone number over concerns about the ease with which lobbyists and business leaders were able to contact him.

The spokesman told Westminster reporters: “We don’t get into details of the advice provided between a Cabinet Secretary and a Prime Minister, and so I’m not going to do that in this instance.”

Labour has demanded that the powerful Liaison Committee of MPs holds an urgent investigation into the Prime Minister’s conduct amid the ongoing row over lobbying.

Shadow chancellor of the Duchy of Lancaster Rachel Reeves called for all correspondence from Mr Johnson’s phone about Government business to be released and for No 10 to release details of communications between ministers, officials and lobbyists.

Sir Bernard Jenkin, chairman of the Commons Liaison Committee made up of select committee chairs, said the committee will consider the request at its meeting on Thursday and will “respond in due course”.

But he added: “The Prime Minster is due to appear before the committee before the summer recess, and at that meeting committee members may question the Prime Minister on any matter.”

The Dyson messages emerged as the Government faces sustained allegations of “cronyism” after a series of reports of former prime minister David Cameron lobbying for his employer, Greensill Capital.

In a statement, Sir James said: “When the Prime Minister rang me to ask Dyson to urgently build ventilators, of course I said yes.

“We were in the midst of a national emergency and I am hugely proud of Dyson’s response – I would do the same again if asked.

“Neither Weybourne nor Dyson received any benefit from the project; indeed commercial projects were delayed, and Dyson voluntarily covered the £20 million of development costs. Not one penny was claimed from any Government, in any jurisdiction, in relation to Covid-19.”