Lawyers described how Mr Hancock may have broken the law regarding coronavirus restrictions, although he admitted only to breaching guidance.
There were also questions about Mrs Coladangelo’s appointment to her role in the Department of Health and Social Care (DHSC) in the first place.
The Prime Minister has so far resisted calls to sack Mr Hancock, who said he was “very sorry” for letting people down after The Sun first reported he was having an extramarital affair.
But Tory Duncan Baker said it was not enough.
Mr Baker told his local newspaper, the Eastern Daily Press: “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.
“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.”
Conservative MP William Wragg tweeted: “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.”
It comes as a snap poll by Savanta ComRes, released hours after photographs of the pair kissing in Mr Hancock’s ministerial office surfaced, found 58 per cent of UK adults feel he should resign, compared to 25 per cent who say he should not.
The Covid-19 Bereaved Families For Justice group, which represents those who have lost loved ones to the pandemic, also called for Mr Hancock to go.
In a letter to the Prime Minister, the group said it has broken its “position of neutrality on ministerial conduct” to urge Mr Johnson to relieve Mr Hancock of his job.
The SNP said Mr Johnson “risks jeopardising vital public health measures” by retaining Mr Hancock as Health Secretary.
The SNP said there are “very serious questions” for Mr Hancock and the incident cannot “simply be brushed under the carpet”.
Its Westminster deputy leader Kirsten Oswald said:”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.
“Despite declaring the matter closed, the reality is that it is anything but closed.
“There are very serious questions for Matt Hancock to answer over the appointment of his aide to the lucrative position, as well as questions over whether or not Hancock broke the ministerial code.”
In a statement on Thursday, Mr Hancock said: “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.”
A Downing Street spokesman said Mr Johnson had accepted Mr Hancock’s apology and “considers the matter closed”.