Boris Johnson has apologised and a senior aide has quit over footage showing Number 10 advisers joking about a Downing Street Christmas party during the coronavirus lockdown.

The Prime Minister has ordered an investigation into claims staff broke lockdown rules by holding a Christmas party last year and told MPs he was “furious” about the footage apparently showing aides laughing about it.

Allegra Stratton, who was the Prime Minister’s spokeswoman, resigned after the leaked clip emerged, offering “profound apologies” and saying she would “regret those remarks for the rest of my days”.

The Prime Minister has repeatedly insisted that rules were followed in Downing Street since the claims first emerged about the December 18 2020 party.

However, at Prime Minister’s Questions in the Commons he said he based that position on assurances from junior staff.

Mr Johnson said he had asked Cabinet Secretary Simon Case “to establish all the facts and to report back as soon as possible – and it goes without saying that if those rules were broken then there will be disciplinary action for all those involved”.

At Prime Minister’s Questions, Mr Johnson said: “I understand and share the anger up and down the country at seeing No 10 staff seeming to make light of lockdown measures, and I can understand how infuriating it must be to think that people who have been setting the rules have not been following the rules because I was also furious to see that clip.

“I apologise unreservedly for the offence that it has caused up and down the country, and I apologise for the impression that it gives.

“But I repeat that I have been repeatedly assured since these allegations emerged that there was no party and that no Covid rules were broken, and that is what I have been repeatedly assured.”

In a tearful statement outside her home, Ms Stratton apologised for her appearance in footage recorded just days after the alleged party.

She had been taking part in a mock press conference in preparation for the planned White House-style televised briefings she would front – a project which was ultimately abandoned.

In the footage obtained by ITV News, Ms Stratton and adviser Ed Oldfield, along with other aides, were filmed joking about a “fictional” Downing Street party.

A laughing Ms Stratton said: “This fictional party was a business meeting … and it was not socially distanced.”

Her appearance in the briefing room was in stark contrast to her emotional statement on Wednesday, where she told reporters: “My remarks seemed to make light of the rules, rules that people were doing everything to obey.

“That was never my intention. I will regret those remarks for the rest of my days and I offer my profound apologies to all of you at home for them.”

Ms Stratton, who had been working as Mr Johnson’s spokeswoman for the Cop26 climate summit, said she understood people’s “anger and frustration”.

“To all of you who lost loved ones, who endured intolerable loneliness and who struggled with your businesses, I am truly sorry and this afternoon I am offering my resignation to the Prime Minister.”

The Prime Minister’s decision to launch an investigation followed a week of official denials that the party took place on December 18 2020, when London was under Tier 3 restrictions – despite reports staff drank alcohol and exchanged Secret Santa gifts.

Downing Street’s official line has now shifted with the announcement of the Case inquiry, with the Prime Minister’s press secretary declining to repeat the statement that “there was no party”.

She said “it wouldn’t be right to comment further” while Mr Case was investigating.

Number 10 would not give a timetable for Mr Case’s investigation to conclude, but the Prime Minister’s official spokesman said “we want it to be as soon as possible”.

Labour leader Sir Keir Starmer said the Prime Minister’s apology “raises more questions than answers” as he had been “caught red-handed”.

He added: “Millions of people now think the Prime Minister was taking them for fools, that they were lied to. They are right aren’t they?”

In response to questioning from Sir Keir, the Prime Minister agreed that any evidence uncovered by the Cabinet Secretary about parties in Downing Street would be handed over to police.

The emergence of the footage of Ms Stratton’s mock press conference fuelled anger on the Tory benches about Mr Johnson’s Number 10 operation.

Scottish Tory leader Douglas Ross said Mr Johnson should quit if he was found to have misled Parliament.

He told Sky News: “If he knew there was a party, if he knew it took place, then he cannot come to the House of Commons and say there was no party.”

In a sign of further potential difficulties for Mr Johnson, his former aide Dominic Cummings – who has become a prominent critic – suggested Mr Case’s investigation should look at parties in the Prime Minister’s Downing Street flat.

Downing Street said Mr Case’s investigation would only look at events related to the December 18 event, rather than a November 13 “flat party” Mr Cummings referred to.