Boris Johnson on Tuesday apologised and said people had a "right to expect better" after he became the first serving Prime Minister in history found to have broken the law.
In a televised statement, Mr Johnson confirmed that he had been fined for attending his 56th birthday party in the Cabinet room of Number 10 during lockdown in breach of rules barring gatherings indoors.
His wife Carrie and Rishi Sunak, the Chancellor, have also been fined for attending the same event on June 19, 2020.
Mr Johnson said it "did not occur" to him that the "brief gathering" was a violation of the rules but added that that he "fully respected" Scotland Yard's decision and had paid the fine.
Mr Sunak has also paid his fine and, in a statement issued several hours after the Prime Minister's, gave an "unreserved apology", saying: "I deeply regret the frustration and anger caused, and I am sorry."
Fourteen Cabinet ministers offered public support to Mr Johnson on Tuesday night, including Michael Gove, Sajid Javid and Liz Truss. However, opposition leaders demanded that Parliament be recalled and said the Prime Minister should resign.
He refused to step down, insisting he felt "an even greater sense of obligation" to stay on to ensure that Vladimir Putin failed in Ukraine and ease the cost-of-living burden in the UK.
Mr Johnson appeared to have weathered the initial storm as three leading MPs who had previously called for his resignation said now was not the right time to remove him.
However, senior Tories warned that he still faced questions over whether he misled the Commons when he denied there was any rule-breaking in Number 10.
Senior Downing Street sources also did not rule out Mr Johnson facing more fines following reports that he attended as many as six of the events under investigation by the Metropolitan Police. More than 50 partygate fines have been issued so far.
Whitehall is braced for the release of the full report into "partygate" by the ethics investigator Sue Gray as early as next week. Sources have told The Telegraph the dossier will be critical of Mr Johnson's conduct and make "uncomfortable reading" for him and a number of senior Whitehall figures.
Its publication will come just a fortnight before the May local elections, with the Tories already braced for losses.
Two snap polls on Tuesday night showed that an overwhelming majority of the public backed calls for Mr Johnson's resignation.
Six in 10 voters in a ComRes polls supported the resignations of both the Prime Minister and the Chancellor, while 57 per cent in a YouGov survey said Mr Johnson should quit and 75 per cent believed he had knowingly lied.
The proportion of Conservative voters who felt he should resign was, however, down from 38 per cent in January to 25 per cent now as senior Tory MPs who had previously demanded he quit withheld judgment – meaning he should remain for the time being.
Sir Roger Gale, one of his most vociferous critics, said Mr Johnson had "effectively misled" the Commons and was "clearly going to have to be held to account", but added that it would be wrong to "unseat" him now.
"The Prime Minister has said categorically no rules were broken and nothing untoward took place. That is patently wrong and he now has to acknowledge that it's wrong," he said. "And he will have to decide where that leaves him in his relationship with Parliament.
"But we are in the middle of an international crisis, and I am not prepared to give Vladimir Putin the comfort of thinking that we are about to unseat the Prime Minister of the United Kingdom and destabilise the coalition against Putin."
Douglas Ross, the Scottish Conservative leader, said the behaviour in Number 10 was "unacceptable" but added that "it wouldn't be right to remove the Prime Minister ... when we need to be united in the face of Russian aggression and the murdering of innocent Ukrainians".
Andrew Bridgen, who like Mr Ross withdrew his letter of no confidence in Mr Johnson, said he was "disappointed that so many in Number 10, including the Prime Minister, were found to have breached rules they set". He said now was "not the time to remove him given the international situation" but warned: "This is not the end of this matter."
However, a former Cabinet minister said the biggest danger for Mr Johnson would be his previous Commons statements denying rule-breaking in Number 10 and "anything that appears to be a deliberate lie".
The former minister said that while a 10-minute birthday party might let him off the hook, other more serious breaches at events he attended could emerge.
"He needs to go to Parliament and eat acres of humble pie and take it on the chin. He must not qualify it but be contrite," he said. "It is not great, but we are not going to get rid of him for now. It still leaves a question mark over who leads us into the next election."
Sir Keir Starmer, the Labour leader and a former director of public prosecutions, demanded the resignations of both Mr Johnson and Mr Sunak as he accused the Prime Minister of "repeatedly" lying about what happened at Number 10.
"The British public made the most unimaginable, heart-wrenching sacrifices, and many were overcome by guilt," he said. "But the guilty men are the Prime Minister and the Chancellor. Britain deserves better – they have to go."
Labour, the Liberal Democrats and SNP called for the Commons to be recalled from the two-week Easter break to allow Mr Johnson to "tender his resignation" to MPs in person. However, that is unlikely as it lies in the Government's gift.
In his statement, Mr Johnson outlined the busy nature of a day on which he had chaired eight meetings in Downing Street and followed them up with a four-hour round trip to a school in Hemel Hempstead, Hertfordshire.
He said: "There was a brief gathering in the Cabinet Room shortly after 2pm, lasting for less than 10 minutes, during which people I work with kindly passed on their good wishes. And I have to say in all frankness at that time it did not occur to me that this might have been a breach of the rules."
The fine is understood to have come as a surprise to Mr Johnson, who added: "I now humbly accept that I was [in breach of the rules]. But I think the best thing I can do now, having settled the fine, is focus on the job in hand. That's what I'm going to do."
Asked whether he had lied when he said "all the guidelines" were followed in Downing Street, he said that "when I said that, I spoke completely in good faith".
Sources close to Carrie Johnson, understood to have attended the birthday party "briefly" with her then new-born baby, confirmed that she had also paid her fine.
A spokesman for Mrs Johnson said: "Whilst she believed that she was acting in accordance with the rules at the time, Mrs Johnson accepts the Metropolitan Police's findings and apologises unreservedly."