Boris Johnson has said he will publish all his text messages with businessman James Dyson.

It has been revealed that the prime minister personally promised Dyson he would “fix” a tax issue after he was directly lobbied by the entrepreneur, who was seeking to build ventilators at the height of the coronavirus crisis.

The BBC reported it had seen a series of text messages between Johnson and Dyson after the business owner was unable to get the assurances he was seeking from the Treasury.

Speaking during PMQs on Wednesday, Labour leader Keir Starmer said the revelations showed it was “one rule for those that have got the prime minister’s phone number, another for everybody else”.

Labour has also said there is “evidence” Johnson breached the ministerial code with the texts.

Johnson, however, said he was “happy to share all the details” of the exchanges as there was “nothing to conceal”.

The texts 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.

Dyson, whose firm is now 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.

But when he failed to receive a reply, the BBC said he took up the matter directly with Johnson.

He wrote in a text that the firm was ready to get to work but that “sadly” it seemed no one wanted them to proceed.

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 Dyson then sought a further assurance, Johnson replied: “James, I am first lord of the Treasury [a statutory post held by the prime minister] and you can take it that we are backing you to do what you need.”

Two weeks later, 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.

Under the ministerial code, ministers are supposed to have an official present when discussing government business and to report back to their department as quickly as possible if a conversation does take place where that is not possible. Johnson claims he informed officials “immediately”.

Challenged about the issue at PMQs, he said: “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.”

SNP Westminster leader Ian Blackford called on Johnson to reveal “how many more Covid contracts he personally fixed” and publish all personal exchanges on these contracts.

The PM said: “There’s absolutely nothing to conceal about this and I am happy to share all the details with the House, as indeed I have shared them with my officials immediately.”

Starmer compared the way Johnson responded to Dyson’s concerns with the government’s treatment of steelworkers, nurses and three million self-employed people who have been left out of coronavirus support schemes.

Nurses “didn’t get a text from the prime minister, they got a kick in the teeth” with a below-inflation NHS pay rise, Starmer said.

What this shows once again is the extent of the sleaze and the cronyism that is at the heart of his Conservative government,” he added.