A spokesman for the Prime Minister said the events were ‘regrettable’.
Two gatherings reportedly took place at Downing Street, with the Prime Minister’s former director of communications James Slack apologising for the “anger and hurt” one of the events – a leaving do held for him – had caused.
A spokesman for the Prime Minister confirmed No 10 has said sorry to the Palace.
The spokesman said: “It is deeply regrettable that this took place at a time of national mourning and No 10 has apologised to the Palace.
“You heard from the PM this week, he’s recognised No 10 should be held to the highest standards, and take responsibility for things we did not get right.”
The day after the events on April 16, 2021, the Queen attended her husband Philip’s funeral wearing a face mask and socially distanced from her family at Windsor Castle, in line with Covid restrictions.
The PM’s spokesman said Boris Johnson was at his country residence Chequers on April 16 and had not been invited to the events.
Asked why No 10 had apologised rather than Mr Johnson himself, his spokesman said: “Well, again, the Prime Minister said earlier misjudgments have been made and it’s right people apologise, as the PM did earlier this week.
“It remains the case that I can’t prejudge the inquiry, which you know is ongoing, which has been led by Sue Gray, but we acknowledge the significant public anger, it was regrettable this took place a time of national mourning.”
It is understood the apology had been delivered via a telephone call through official channels.
It comes after Mr Slack, who until last year was Mr Johnson’s director of communications, apologised on Friday morning for the “anger and hurt” his leaving party had caused.
Mr Slack, who is now deputy editor-in-chief of The Sun newspaper, said he took “full responsibility” and was “deeply sorry”.
In an emailed statement issued by The Sun’s publisher, News UK, he added: “This event should not have happened at the time that it did.”
His party was one of two reported to have taken place that evening, which started separately and later merged.
The Daily Telegraph reported accounts from witnesses, who said alcohol was drunk and guests danced to music, with a person sent to a local shop with a suitcase to buy wine.
A Downing Street spokesperson said of Mr Slack’s event: “On this individual’s last day he gave a farewell speech to thank each team for the work they had done to support him, both those who had to be in the office for work and on a screen for those working from home.”
Conservative MP Sir Roger Gale said the gatherings were “wholly unacceptable” and confirmed he had submitted a letter of no confidence in Mr Johnson to the 1922 Committee of backbench MPs.
On Thursday evening his Tory colleague Andrew Bridgen became the fifth MP to have publicly said they had written to committee chairman Sir Graham Brady.
The Telegraph reported that as many as 30 letters have been submitted so far, with a total of 54 needed to trigger a vote.
However, Foreign Secretary Liz Truss said people should “move on” following Mr Johnson’s apology over a previous bash on Wednesday.
Senior Conservative MP Julian Knight told Times Radio: “What I would say is that it will be charitable to say that partygate, if you like, is due to acts of extreme stupidity on behalf of those at No 10.”
Asked if that meant he thought the Prime Minister had been stupid, he said it applied to “anyone involved”.
Meanwhile, a councillor from the Sutton Coldfield Conservatives, an association in a safe Tory seat which withdrew its support for Mr Johnson on Thursday, said the move reflected “local views at the very grassroots levels”.
Councillor Simon Ward told BBC Radio 4’s Today programme: “The conversation we had last night … was really about what I think we have the right to expect from our leaders and the standards of leadership we expect from them, and the trust that we put in them.”
At the time of the two newly-reported gatherings on April 16, Government guidance said: “You must not socialise indoors except with your household or support bubble. You can meet outdoors, including in gardens, in groups of six people or two households.”
It brings the total number of parties or gatherings alleged to have happened across Whitehall during restrictions to 14.
On Wednesday, the Prime Minister apologised for attending a “bring your own booze” party in the Downing Street garden in May 2020, during the first coronavirus lockdown, but insisted he believed it was a work event and could “technically” have been within the rules.
Members of the Government urged Mr Johnson’s critics to wait for the findings of senior official Sue Gray’s inquiry before passing judgment after Tory MPs began publicly calling for him to quit.
The Times reported that the inquiry was expected to find no evidence of criminality but that the investigation could censure Mr Johnson for a lack of judgment.
The newspaper said Ms Gray was expected to avoid concluding whether the Prime Minister breached the ministerial code, as this would fall outside her remit.
But she is set criticise the culture in Downing Street, it said.
The Metropolitan Police said there is no change to its position on investigating Downing Street parties amid fresh allegations of more gatherings taking place.