Oliver Dowden, the ruling party’s chairman, hinted at a possible shake-up by saying Mr Johnson was committed to addressing the drinking and partying culture at Number 10 Downing Street, which surfaced with revelations of raucous gatherings in the garden while England was in lockdown.
It is believed Mr Johnson plans to weed out aides who played a role in the public relations disaster.
The UK’s Sunday Times newspaper reported that Martin Reynolds, his principal private secretary and a former ambassador to Libya, is among the probable targets.
He organised a picnic on May 20, 2020, when England was in lockdown, inviting 100 people to the Downing Street garden to bask in the sunshine with nibbles and alcoholic drinks.
Others braced for sackings include Mr Reynolds’ deputy, Stuart Glassborow, and Dan Rosenfield, Downing Street’s chief of staff.
Mr Johnson is reported to have drawn up a plan to win back public support with measures such as banning alcohol at No 10 Downing Street to curb its drinking culture.
Mr Dowden said the Conservatives needed to “up our game” going forward.
In an interview with BBC One’s Sunday Morning programme, he said a culture change was needed.
He said he was “disgusted” to learn that aides had spent the night before the Duke of Edinburgh’s funeral drinking and dancing in Downing Street.
“He is very much apologetic for this happening,” Mr Dowden said of Mr Johnson. “It shouldn’t have happened.
“The task for us now is to make sure that we address the underlying culture in Downing Street and I know that the prime minister is completely committed to doing that.”
“There were failings. We should have done better – much, much better. We need to up our game, and that needs to be addressed.”
But despite working in the building throughout the pandemic, Mr Dowden said he was not aware of the party culture until the allegations came to light.
Mr Dowden served as culture secretary from February 2020 to September 2021, in which time several parties took place in the Downing Street garden.
On the evening of May 20, 2020, Mr Dowden led the daily government press conference to explain coronavirus rules to the public.
At about the same time, staff would have been preparing for the “bring your own booze” party, which the prime minister has apologised for attending.
Mr Dowden said he knew nothing about the event and said he left the building soon after concluding the televised briefing.
Tony Blair, the former Labour prime minister, said he could “understand how” parties in No 10 could happen during lockdown, but that they were still inexcusable.
Mr Blair, who occupied Downing Street for a decade, said he did not want to “get into questions of resignation or not”, when asked whether Mr Johnson should resign over the matter.
He said he could “understand people feeling enraged and very angry” about the parties, which allegedly breached Covid-19 rules, but that he could also see it “from the perspective of Downing Street”.
“The people in Downing Street would have been working under the most enormous pressure, enormous difficulty,” Mr Blair told Times Radio.
“I understand how it happened.
“But the trouble is, you can give an explanation but you can’t really excuse it.
“People were obeying restrictions, often with massive personal cost and anguish and grief, and it just shouldn’t be allowed to happen, frankly.
“But I guess he [Mr Johnson] knows that.”
On Saturday, former children’s minister Tim Loughton became the sixth Conservative MP to urge Mr Johnson to resign, accusing him of inflicting irreversible “terminal damage” on the party.
He rejected the idea that firing staff or changing policies could save Mr Johnson’s embattled premiership.
“It is not down to a simple government policy change or a sacking of ministers or officials to put things right,” Mr Loughton said on Facebook.
“In this case, all roads lead back to Downing Street and the person whose name is on the front door.”