Both Mr Johnson and Chancellor Rishi Sunak have been hit with criminal sanctions for attending the gathering in the Cabinet Room to mark the Prime Minister’s 56th birthday on June 19 2020.
The pair apologised on Tuesday and confirmed they had paid the fines imposed by the Metropolitan Police.
But they resisted calls for their resignations – insisting they were keen to now get on with the job.
Transport Secretary Grant Shapps defended the Prime Minister on Wednesday morning, saying he is “human” and did not knowingly break the law.
Asked on Sky News how Mr Johnson can “possibly remain in office”, he said: “Everyone is human, people sometimes make mistakes.”
It comes as dozens of Tory MPs have shown their support for the Prime Minister on social media, with cabinet ministers praising his leadership during Covid and Brexit and pointing to the war in Ukraine.
By contrast, Labour has joined a chorus of demands for the Commons to be recalled from its two-week Easter break to allow the PM to “tender his resignation” in person to MPs.
The latest fines came in a further tranche of fixed penalty notices (FPNs) announced by Scotland Yard in relation to Operation Hillman, which is probing possible Covid breaches in Downing Street and Whitehall.
More than 50 fines have been referred to the Acro Criminal Records Office since the inquiry started.
Mr Johnson did not rule out the prospect he could be fined again for further events.
He is reported to have attended six of the 12 under investigation.
Speaking to Sky News about the PM’s fine, Mr Shapps said Mr Johnson is “incredibly embarrassed by the whole thing”.
“It has been a very high-profile job and quite rightly, the police are investigating, they independently come to their view,” he said.
“He has apologised, he has accepted responsibility. He has paid a 50 quid fine.
“The question I suppose, your question goes to the heart of, you know: did he set out to do this? Was it something that was done with malice, with intent?
“And the answer of course, is no. It’s something that happened in error, and as I have said, I’ve spoken to him, he is incredibly embarrassed by the whole thing.
“He knows that it was stupid, indefensible. But he didn’t set out to break the law, and he has paid the fixed penalty notice fine, and has a very big job to do.”
When asked what it will take for the Prime Minister to leave office, Mr Shapps said: “We live in a democracy and people have every right to vote, to decide what happens with their representatives.”
It also emerged on Tuesday that Carrie Johnson, Mr Johnson’s wife, had received and paid a fine linked to the event on June 19 2020, at which, according to Northern Ireland minister Conor Burns, the Prime Minister was “ambushed with a cake”.
Reports have suggested that up to 30 people attended the do and sang Happy Birthday.
Labour’s shadow chancellor, Rachel Reeves, said Mr Johnson and Mr Sunak did not seem to understand how “deeply offensive” their rule breaches were, as she called for “fresh leadership”.
She said the Prime Minister’s claim that he unknowingly broke the rules was not a sufficient explanation, telling BBC Radio 4’s Today programme: “He is still obfuscating and saying, oh he still didn’t really realise he was breaking the rules and he just happened to be in this room at the time… It’s just not good enough.
“People have never made, collectively or personally, the sacrifices that were made during the pandemic outside of wartime and the Prime Minister and the Chancellor still don’t seem to understand how deeply offensive it is, especially to those who lost loved ones, or who were not there for the birth of their child, or for the death of a loved one.”
On whether Parliament might be recalled to discuss the issue, as urged by Labour, Mr Shapps told BBC Breakfast: “We meet again next week; it’s Easter weekend in between. So, there will be plenty of opportunity. The Opposition are doing what you’d expect the Opposition to do and that’s absolutely fine.”
Speaking to broadcasters at his country residence, Chequers, on Tuesday, Mr Johnson said it “did not occur” to him at the time that the party for which he was fined might be breaching Covid rules.
“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,” he said.
“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.”
He added: “I now humbly accept that I was. But I think the best thing I can do now is, having settled the fine, is focus on the job in hand. That’s what I’m going to do.”
Asked if he thought more fines were coming his way, he said the media would be among the first to know.
Rishi Sunak offered an “unreserved apology”, saying he understood that “for figures in public office, the rules must be applied stringently in order to maintain public confidence”.
“Like the Prime Minister, I am focused on delivering for the British people at this challenging time,” the Chancellor said.
A spokesperson 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.”