A minister warned a senior official that ventilators might need to be bought from Sir James Dyson “so that he [could] then market [them] internationally” as “being used in UK hospitals” after the businessman spoke to Boris Johnson, the Covid inquiry has heard.

The message from Lord Agnew, a Tory Treasury minister, to the government’s chief commercial officer, Gareth Rhys Williams, emerged as the public inquiry into the pandemic started a four-week examination of procurement.

The inquiry has faced criticism ahead of its latest hearings for failing to call suppliers of equipment so that they may be questioned about their conduct after evidence emerged of some companies and individuals profiting from the global crisis.

In his opening submission on procurement, Pete Weatherby KC, representing the Covid-19 Bereaved Families for Justice UK, lamented the lack of opportunity to question suppliers about the role of political patronage in securing contracts.

Weatherby said that among those whose evidence would not be heard would be David Meller of Meller Designs, a donor to Michael Gove’s 2016 leadership bid, whose fashion house was referred to a VIP lane of PPE suppliers by the cabinet minister.

The barrister then raised the case of Dyson, whose company was not referred to the VIP lane and did not provide PPE.

Dyson received a provisional order for 10,000 of for his prototype ventilator, called CoVent, in early 2020, after he responded to a call from Johnson for industry to step in amid a shortage.

It has previously emerged via leaked text messages that Dyson, who was a backer of Brexit, personally lobbied Johnson to ensure the firm and “senior individuals” would not have to pay extra tax if they came to the UK to make ventilators during the pandemic.

The government did not buy Dyson’s ventilators but Weatherby informed the inquiry of the existence of a communication between Agnew and Rhys Williams.

“With respect to Mr Dyson, he was apparently championed by both Mr Gove and the then prime minister, Mr Johnson,” Weatherby said. “Mr Dyson is the well-known vacuum manufacturer. He took part in the ventilator challenge.

“By April, it was clear that his model would not be pursued due to clinical viability and functionality. Nevertheless, Lord Agnew, a minister, warned the government chief commercial officer, Gareth Rhys Williams, in the following terms: ‘We’re going to have to handle Dyson carefully. I suspect we’ll have to buy a few machines, get them into hospitals so that he can then market internationally, being able to say that they are being used in UK hospitals. We both need to accept that it will be a bigger decision than we can both make. Remember, he got a personal call from the PM. This can’t be ignored’.”

Weatherby told the inquiry that the procurement expert Prof Albert Sanchez Graells had described the manner on which Dyson was treated as an “affront to the procurement rules”.

A Dyson spokesperson said: “Sir James Dyson responded to a personal call from the prime minister of the United Kingdom, to develop and make a medical-grade ventilator in 30 days during the national emergency.

“Dyson had no intention of manufacturing ventilators for profit. Far from receiving any commercial benefit, there was significant commercial cost to Dyson, which diverted 450 engineers away from commercial projects.

“Mercifully, treatments changed, and mass use of ventilators was no longer seen as an effective remedy, the UK government cancelled the order it had placed, and none were ever sold overseas.

“Uniquely among the many businesses involved, James Dyson did not seek payment for any of the £20m the company spent on the project – rather this was its contribution to the national effort to save lives. In addition, Dyson did not claim any furlough money, subsidy, or government loans related to the Covid-19 pandemic anywhere in the world.”

Earlier in the day, the inquiry chair, Heather Hallett, a former court of appeal judge, said she would hold a special closed session about PPE Medpro, the firm linked to Michelle Mone and her husband, Doug Barrowman, to avoid prejudicing a criminal inquiry by the National Crime Agency.

It also emerged that the company, along with Mone and Barrowman, had applied for “core participant” status at the inquiry alongside groups such as bereaved families and the British Medical Association, giving them special rights including disclosure of documents and ability to make statements.

Lady Hallett said she had rejected the application, which came 468 days after the deadline. “I do not accept that applicants have a direct or significant role in the matters to be investigated by the inquiry,” she said.

Mone and Barrowman both deny wrongdoing.