Matt Hancock is coming under relentless pressure to quit as MPs warned that the health secretary’s rule-breaking tryst with a colleague risked becoming as toxic to voters as Dominic Cummings’ drive to Durham. Hancock apologised for breaching social distancing guidelines after the Sun newspaper obtained footage from 6 May of him in a clinch with Gina Coladangelo, a non-executive director at the Department of Health and Social Care. The health secretary appealed for “privacy” to deal with this “personal matter”, and Downing Street said the prime minister had accepted Hancock’s apology for breaking the rules, and “considers the matter closed”. Hancock, who has been married to his wife for 15 years, is facing fresh questions about how Coladangelo – a friend from his days at Oxford University – came to be hired, and whether they were already in an intimate relationship at that point. Labour’s deputy leader, Angela Rayner, has written to Boris Johnson’s independent adviser on ministerial interests, Lord Geidt, calling on him to investigate the apparent conflict of interest. Families bereaved by Covid wrote to the prime minister, urging him to sack the health secretary. Hannah Brady, whose father, Shaun Brady, 55, died in May 2020, wrote: “To allow Matt Hancock to continue to hold the position of health secretary compounds the heartbreak of bereaved families who sacrificed so much whilst he broke the rules. “It is not only an insult to bereaved families and all those who have obeyed the rules, but undermines the public’s trust in measures designed to save others from the loss we have suffered.” She concluded: “If Matt Hancock is unable to find the decency to do the right thing and resign his position, it is paramount that you relieve him of it.” Conservative MPs said they were already beginning to receive angry messages from constituents about Hancock’s public rule-breach, and expected more. “Usually these things tend to build over the weekend,” one backbencher said, while several conceded that they were braced for something like the wave of public anger that followed the revelation of Cummings’ Barnard Castle jaunt. “There will be anger, because he broke his own rules,” said a former cabinet minister. Another MP said: “People can’t abide a double standard.” A snap poll by YouGov found that 49% of those surveyed thought Hancock should step down, up from 36% in May. Behavioural scientists advising the government warned that the health secretary’s public disregard for the social distancing rules could undermine public compliance. “‘Do what I do’ can have a bigger impact than ‘Do what I say’, particularly when combined with public anger,” said John Drury, a professor of social psychology at the University of Sussex and a member of the Sage subcommittee advising on behavioural science, Spi-B. “We know from research on the Cummings incident that rule-breaking at the top undermines social cohesion and adherence.” On Friday night the Sun released a video, apparently taken on CCTV and one minute 10 seconds long, showing Hancock looking out of a room, before closing the door, standing in front of it and kissing Coladangelo. The photographs were apparently taken on 6 May, before social distancing rules were eased on 17 May to allow hugging. Indoor gatherings between members of different households remained illegal at that point, but Hancock’s aides insist no law was broken because the pair were in the department for legitimate work purposes. The Metropolitan police said they would not investigate Hancock over any alleged Covid rule breaches. The force said it was “aware of the distribution of images alleged to have been obtained within an official government premises”. It added: “No criminal investigation has been launched. At this time this remains a matter for the relevant government department.” Coladangelo helped on Hancock’s 2019 leadership campaign, attending meetings with the media alongside him. Parliamentary records show that in June 2019, he sponsored her for a parliamentary pass, allowing her to come and go at Westminster, which she received under her married name, Gina Tress. Her husband, Oliver Tress, is the founder and head of Oliver Bonas. She was formerly an executive for the PR and lobbying firm Luther Pendragon. In November last year, Labour complained about apparent cronyism after it emerged that Coladangelo had first been made an unpaid adviser at the DHSC and then a non-executive director, a part-time role paid £15,000 a year. Answering questions from the media, Johnson’s spokesperson declined to say whether No 10 was concerned whether their relationship constituted a conflict of interest, or if he broke the law on Covid rules. Hancock said in a statement: “I accept that I breached the social distancing guidance in these circumstances. I have let people down and am very sorry. I remain focused on working to get the country out of this pandemic, and would be grateful for privacy for my family on this personal matter.” Johnson’s spokesperson said: “You’ve seen the health secretary’s statement, so I would point you to that. I don’t really have anything to add. The health secretary set out that he accepted he breached the social distancing guidelines, and he has apologised for that. The prime minister has accepted the health secretary’s apology and considers the matter closed.” Rayner suggested Hancock may have broken the ministerial code by not declaring his relationship with Coladangelo, and urged the prime minister to sack him. Hancock’s predicament is an early test for Geidt, who was appointed after his predecessor, Alex Allan, resigned because Johnson chose to ignore his finding that Priti Patel had breached the ministerial code. According to points 7.1 and 7.2 of the code, “ministers must ensure that no conflict arises, or could reasonably be perceived to arise, between their public duties and their private interests, financial or otherwise”. But some Conservative MPs said they were anxious. One said: “It just doesn’t sit right. I thought that the moment I heard about it. It’s not that we don’t make mistakes in our personal lives, but it’s very difficult if the minister telling people they can’t visit their grandparents or go to sports days is then found snogging his non-executive director in the office. “It’s the sense of unfairness that makes it so bad. People can’t abide a double standard.” Last year when Prof Neil Ferguson, the epidemiologist who has helped shape the government’s response to coronavirus, quit his advisory role for breaking social distancing rules by having a woman visit him at his home, Hancock said he would support the idea of police taking action against him.