Sir James Dyson has said it is "absurd to suggest" his company was doing anything other than trying to follow the rules, after it was reported that the prime minister personally promised him he would "fix" an issue over the tax status of his employees.
The BBC reported that it had seen a series of text messages between the pair after Sir James was unable to get the assurances he was seeking from the Treasury.
It said the conversations took place last March in the early stages of the COVID-19 pandemic.
At the time, the government was appealing to companies to supply ventilators in case the NHS ran out.
Labour said the revelations were "jaw-dropping" and declared: "Tory sleaze has reached the heart of Downing Street."
Responding to the report, the government said it was right to secure equipment for the health service in "extraordinary times".
And in a statement sent to Sky News, 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.
"Our ventilator cost Dyson £20m, 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 nor Dyson received any benefit from the project, indeed commercial projects were delayed, and Dyson voluntarily covered the £20m of development costs.
"Not one penny was claimed from any government, in any jurisdiction, in relation to COVID-19."
A government spokesman said: "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.
"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."
Responding to the report, a Labour spokesperson 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."
Sir James, whose company is based in Singapore, wrote to the Treasury seeking assurances that his staff would not have to pay more tax if they came to the UK to help with the ventilators project.
The BBC reported that when he did not receive a response, Sir James raised the issue personally with the PM.
He said in a text that his company was ready but "sadly" it seemed like no-one wanted them to proceed.
Mr Johnson messaged back: "I will fix it tomo! We need you. It looks fantastic."
He texted Sir James, again, saying: "[Chancellor] Rishi [Sunak] says it is fixed!! We need you here."
When he sought further assurance, the PM said: "James, I am First Lord of the Treasury and you can take it that we are backing you to do what you need."
Speaking at the Treasury Select Committee two weeks later, Mr Sunak said the tax status of those who arrived to provide specific help during the pandemic would not be affected.
The Dyson revelation comes after a range of disclosures about former PM David Cameron’s activities on behalf of Greensill Capital, which has prompted Mr Johnson to order a review led by top lawyer Nigel Boardman.