Cabinet members who were at Tuesday’s National Security Council (NSC) have been sent an ultimatum by Whitehall’s most powerful official to confess or deny whether they leaked a controversial decision to allow Chinese telecoms firm Huawei to help build the UK’s 5G phone network.

Cabinet secretary Sir Mark Sedwill is understood to have written to those present and demanded that they tell him by 2pm on Thursday whether they were involved and would be willing to cooperate with an inquiry, prompting the five prime suspects to scramble to “categorically deny” that they were behind the leak.

The move came at an acutely sensitive time as several of those present are hoping to take over as prime minister when Theresa May steps down. There are also growing calls for whoever did leak the information to the Daily Telegraph to be prosecuted under the Official Secrets Act.

Sedwill also asked the senior ministers present to agree that their special advisers, and any officials who had access to information about the outcome of the NSC meeting, would also assist the inquiry.

The NSC meeting had decided to allow Huawei to supply some “non core” telecoms equipment for next-generation phone networks in the UK and the initial focus over the leak has centred on the five ministers present who were opposed to Huawei’s having any involvement in 5G.

Jeremy Hunt, the foreign secretary, was the first to go public on Thursday in denying he was behind the leak, condemning it at a lunch of the parliamentary press gallery. He said it was was “utterly appalling” and said denied that he or any of his staff were involved.

The leadership candidate added: “I – as I think everyone here knows – have never leaked confidential cabinet discussions and I never will, so I don’t want to comment further. But I do think it is a very, very bad day for our democratic processes.”

Shortly after, Gavin Williamson, the defence secretary, released his own statement of denial. He said: “Neither I nor any of my team have divulged information from the National Security Council.”

Sources close to Penny Mordaunt, the development secretary, then said she “categorically denied” being involved in the leak – a statement that was echoed shortly after by allies of the trade secretary Liam Fox.

Finally, Sajid Javid, the home secretary, and another leadership contender, denied being involved. He also said: “For any cabinet minister or any minister in the government to share sensitive information in the public domain is completely unacceptable and it should be looked at.”

Jeremy Hunt and Gavin Williamson leaving Downing Street. Both have denied leaking details of the NSC meeting. Photograph: Toby Melville/Reuters
Sedwill’s inquiry began with a letter to the members of the NSC – a secret official body comprising the prime minister, nine cabinet members, spy chiefs and senior members of the armed forces. Phone and email records could be examined and people questioned if it develops further and even lead to a minister or aide being fired.

Former cabinet secretary Gus O’Donnell, who helped set up the NSC, said the leak was “incredibly serious” and a “complete outrage”. “If I were cabinet secretary and I thoroughly applaud what my successor Mark Sedwill has done is to say ‘look, this is just beyond the pale’ – this is really important for the country, these issues are massively important,” he told BBC Radio 4’s Today programme.

Former defence secretary Michael Fallon said on Thursday that Downing Street should call in the police and mount a “a proper Scotland Yard investigation” and Andrew Mitchell, the Tory MP for Sutton Coldfield, told the BBC’s Newsnight that MI5 should be asked to help.

No 10 reacted with anger and alarm after the Huawei decision was leaked. It follows a series of leaks from cabinet and other sensitive political meetings as May’s authority has collapsed during the Brexit crisis, but none from the NSC. Insiders said it is a place where “politicians, intelligence agencies and military chiefs are supposed to be able to discuss issues openly and informally”, saying that the leak has eroded trust.

Politicians present had been deadlocked at five apiece, with the decision only being made after what amounted to a casting vote from the prime minister. Those who spoke against the plan argued for a blanket ban on Huawei telecoms equipment.

A public announcement of the decision had not been due for several weeks, after further work was undertaken on various additional safeguards, but the leak transformed the debate with several backbench Conservatives raising concerns on Wednesday and Thursday.

The five ministers in favour of allowing Huawei to supply equipment to “non core” parts of the network, such as antennas, were led by May but also included David Lidington, the Cabinet Office minister, Philip Hammond, the chancellor, Greg Clark, the business secretary, and Jeremy Wright, the culture secretary.

It is understood that the final decision was in line with the advice from Britain’s intelligence agencies, led by GCHQ’s National Cyber Security Centre, which already monitors Huawei technology in case of a backdoor that could be exploited by the Chinese government.

The spy agency has repeatedly said Huawei must be monitored but that the risks can be contained. But politicians concerned about the company said the UK should heed warnings from US and Australian spy agencies, who share intelligence with the UK as part of the Five Eyes network.

Tom Tugendhat, the chair of the foreign affairs select committee, told MPs: “This is fundamentally a diplomatic and political question, just as much as a technical one, and … respecting our Five Eyes partners is an essential part of the decision.”

Earlier Labour demanded “a full leak inquiry” in an urgent question in the House of Commons. Jo Platt, the shadow minister for the Cabinet Office, said: “If a minister did leak this information they are not fit to serve in the cabinet and they are certainly not fit to be prime minister.”

In the debate that followed, Wright condemned the leak and signalled that a criminal investigation under the Official Secrets Act could yet go ahead. He told MPs “I cannot rule it out”, and added it was “a matter for investigating and prosecuting authorities to consider”.

Hammond is in China to participate in an investment forum in Bejing. On Thursday he met Hu Chunhua, the country’s vice-premier, but it is understood that the subject of Huawei was not raised by either side.