The health secretary has resigned after photos and a video emerged of him breaking lockdown rules with his government aide, Gina Coladangelo.
Writing to prime minister Boris Johnson, Hancock said the government “owes it to people who have sacrificed so much in this pandemic to be honest when we have let them down”.
He said: “The last thing I would want is for my private life to distract attention from the single-minded focus that is leading us out of this crisis.
“I want to reiterate my apology for breaking the guidance, and apologise to my family and loved ones for putting them through this.
“I also need to be with my children at this time.”
“It has been the honour of my life to serve in your cabinet as secretary of state and I am incredibly proud of what we have achieved.
“I will of course continue to support you in whatever way I can from the back benches, and I would like to thank you for your unwavering support, your leadership and your optimism, particularly as we worked together to overcome this awful disease,” he added.
Matt Hancock’s resignation comes after several Tory MPs joined calls for him to quit.
Hancock apologised after The Sun revealed he was having an affair, but Tory MP Duncan Baker said the apology was not enough.
“In my view people in high public office and great positions of responsibility should act with the appropriate morals and ethics that come with that role,” the Norwich MP told Eastern Daily Press.
Baker added: “Matt Hancock, on a number of measures, has fallen short of that. As an MP who is a devoted family man, married for 12 years with a wonderful wife and children, standards and integrity matter to me.
“I will not in any shape condone this behaviour and I have in the strongest possible terms told the government what I think.”
Tory MP Esther McVey told GB News: “If it would have been me, I would have resigned myself, and I said that for Dominic [Cummings], and I’m hoping that Matt Hancock is thinking the same thing, that he doesn’t have to have it pushed upon him.”
William Wragg, Tory MP for Hazel Grove and chairman of the Commons Public Administration and Constitutional Affairs Select Committee, said: “Re Mr Hancock, a thought: Covid regulations have created a dystopian world of denunciation, finger-wagging & hypocrisy.
“Let us be freed from this tyranny of diktat and arbitrary rule. As we shall inevitably see with this sad example, the revolution always consumes its own.”
Tim Montgomerie, a Conservative commentator and former adviser to Mr Johnson, told the BBC’s Today programme: “When you undermine your own rules, you have to show the public that you understand the transgression you’ve made and you resign.”
The Scottish National Party said Boris Johnson clinging onto Hancock was putting “vital public health measures” at risk.
Boris Johnson’s spokesperson said on Friday the prime minister had accepted Hancock’s apology for breaching coronavirus lockdown restrictions and “considers the matter closed.”
In response, the SNP said what happened cannot “simply be brushed under the carpet” and warned there are “very serious questions” for Hancock.
SNP deputy Westminster leader Kirsten Oswald said: “Boris Johnson risks jeopardising the vital public health measures in place the longer he desperately clings on to his shamed Health Secretary – just like he did with Dominic Cummings.
“The Prime Minister must at long last do the right thing and put his responsibilities to public health first.
“There must be public confidence in those setting the rules and it cannot be the case that it is one rule for the Tory elite and another for the rest of us.
Related: Sack Hancock or risk health measures, SNP tells Johnson
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