Boris Johnson personally promised Sir James Dyson he would “fix” an issue over the tax status of his employees after he was directly lobbied by the entrepreneur, it has been reported.

The BBC said it has seen a series of text messages between the two men after Sir James was unable to get the assurances he was seeking from the Treasury.

The exchanges took place in March last year at the start of the pandemic when the Government was appealing to firms to supply ventilators amid fears the NHS could run out.

I am First Lord of the Treasury and you can take it that we are backing you to do what you need

The Government said it was right to secure equipment for the NHS in “extraordinary times” while Sir James said it was “absurd to suggest that his firm was doing anything other than seeking to comply with Treasury rules”.

Labour, however, described the disclosures as “jaw-dropping” and said Mr Johnson must now agree to a full, independent inquiry into lobbying.

Sir James, whose firm is now based in Singapore, wrote to the Treasury asking for an assurance that his staff would not have to pay additional tax if they came to the UK to work on the project.

However, when he failed to receive a reply, the BBC said he 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.

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.”

When Sir James then sought a further assurance, Mr Johnson replied: “James, I am First Lord of the Treasury and you can take it that we are backing you to do what you need.”

As the public would expect, we did everything we could in extraordinary times to protect our citizens and get access to the right medical equipment

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.

A Government spokesman said it was right to take action in “extraordinary times” to ensure the NHS had the equipment it needed.

“At the height of the pandemic, there were genuine fears that we would quickly run out of ventilators, leaving the NHS unable to treat patients and putting many lives at risk,” the spokesman said.

“As the public would expect, we did everything we could in extraordinary times to protect our citizens and get access to the right medical equipment.”

Under the ministerial code, ministers are supposed to have an official present when discussing government business and to report pack to their department as quickly as possible if a conversation does take place where that is not possible.

Culture Secretary Oliver Dowden defended the Prime Minister’s actions saying that it had been necessary to move “at pace” in a national crisis.

He said the “concession” on the tax rules had been for a very short period only and was reported to Parliament.

“This was not some sort of concession specifically to James Dyson or his employees,” he told the BBC Radio 4 Today programme.

“It was a wider concession for a short period of time that applied to a range of people that were involved in medicine, in ventilator production, for that short period of crisis.”

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.

The report comes amid intensive controversy at Westminster over lobbying following the disclosures of David Cameron’s activities on behalf of the failed finance firm, Greensill Capital.

In response, Mr Johnson ordered a review by senior lawyer, Nigel Boardman.

A Labour Party spokesman said: “These are jaw-dropping revelations. Boris Johnson is now front and centre of the biggest lobbying scandal in a generation, and Tory sleaze has reached the heart of Downing Street.

“The Prime Minister appears to have used the power of his office to personally hand public money to a billionaire friend in the form of tax breaks. If true, it is clearer than ever there is one rule for the Conservatives and their friends, another for everyone else.

“The stench of sleaze has been building up around this Conservative Government for months. Boris Johnson must now agree to a full, transparent and independent inquiry into lobbying – and end the scandal of Conservative politicians abusing taxpayer money.”

Public Accounts Committee chairwoman, Meg Hillier, a Labour MP, said: “We’ve seen people have criticised in the past ‘sofa government’ for being too informal. Well, that seems to have been replaced with ‘WhatsApp government’.”

She told Times Radio she had concerns about “privileged access” to the Prime Minister and it was “shocking” that he was now embroiled in the lobbying row.

“Everyone should have the same access and the Government was having to make fast decisions and was being lobbied by everybody, MPs, lots of organisations – that’s fair enough – but it should not be down to the Prime Minister making these simple guarantees himself without going through proper processes.”