Prime Minister Theresa May's two closest advisers have quit after the Conservatives failed to win a majority of MPs in the general election.
The BBC understands the PM was warned she faced a leadership challenge unless she sacked Nick Timothy and Fiona Hill.
Labour said the pair had "taken the fall" for the prime minister.
Mrs May has announced that the new Downing Street chief of staff is ex-Conservative MP and former housing minister Gavin Barwell.
Mr Timothy said he took responsibility for his role in the "disappointing" result and the widely-criticised manifesto package on social care.
The BBC's assistant political editor Norman Smith said the pair's departure bought the PM some "breathing space" following 24 hours of recriminations after the Conservatives lost their overall majority.
He said the two were so close to the PM that critical MPs believed that, unless they made way, she would not be able to change her leadership style to adopt a more "outgoing, inclusive, responsive, empathetic approach".
Mrs May has said she intends to stay as prime minister and on Saturday evening it was announced her party's chief whip had agreed an outline deal "in principle" with the DUP of Northern Ireland, which would see the unionist party support the Tories on key votes.
Mr Timothy and Ms Hill both stepped down amid mounting pressure on Mrs May to overhaul the way No 10 worked and broaden her circle of advisers.
Announcing his resignation on the Conservative Home website, Mr Timothy urged Tory MPs to "get behind" Mrs May but said nothing should be allowed to get in the way of the process of forming a government and beginning Brexit talks.
He said the Conservatives' failure to win was not due to a lack of support for Theresa May and the Conservatives but due to an "unexpected surge" of support for Labour.
Who were the PM's special advisers?
Fiona Hill: Fiercely loyal and seen as a formidable operator, Fiona Hill was at Mrs May's side for four years at the Home Office, becoming a close confidante of the then home secretary. A former Sky News and Scotsman journalist in her 40s, she led work on the Modern Slavery Act and published her own report on the subject.
She was forced to resign as Mrs May's special adviser in a 2014 dispute with Michael Gove over who was to blame for briefing newspapers about an increase in extremism in schools. But she was brought back into the fold when Mrs May became PM.
Nick Timothy: The bearded Brummie is the son of a steelworker, who went to grammar school and joined the Conservative Party at the age of 17. He is credited with influencing the PM's views on social mobility and the need to put the Conservatives "at the service of working people".
His ambition to be a Conservative MP was reportedly thwarted by David Cameron, following a row over special advisers being asked to canvass in a by-election.
He conceded his party had failed to communicate a sufficiently "positive" message to voters and address their concerns over years of austerity and inter-generational divisions, including over Brexit.
"We were not talking to the people who decided to vote for Labour," he said.
He defended the party's "honest and strong" manifesto, saying controversial proposals to use the value of peoples' homes to fund domiciliary care costs had been discussed in government for months and were not his own personal "pet project".
But he added he took "responsibility for my part in this election campaign, which was the oversight of our policy programme" and "I regret the decision not to include in the manifesto a ceiling as well as a floor in our proposal to help meet the increasing cost of social care".
Ms Hill said it had been a pleasure to serve in government and she believed Mrs May would continue as prime minister.
Norman Smith said he understood that senior Conservatives had warned the PM they would instigate a leadership contest at a meeting of backbenchers early next week if the pair did not leave, and were confident they could get the required 48 signatures to trigger a contest.
One former minister, Anna Soubry, welcomed the clearout, saying it was the "right thing to do" and saying the PM must "build a consensus" on Brexit and other issues.
But Labour's deputy leader Tom Watson said the PM's advisers had "taken the fall" for her but tweeted the PM was "responsible for her own defeat".
Mr Barwell lost his Croydon Central seat on Thursday - which he won in 2015 with a majority of just 165 votes - to Labour's Sarah Jones, polling 24,221 votes to Ms Jones's 29,873.
He has written a book entitled How to Win a Marginal Seat: My Year Fighting For My Political Life.
He was appointed Minister for Housing and Minister for London in July 2016.
Earlier, Mrs May's director of communications until the election was announced, Katie Perrior, called the campaign "pretty dysfunctional", telling the BBC she "needed to have a few grey hairs in there who been around a bit and could say 'don't do that'".
As the Conservative leadership begins formal negotiations with the DUP, disquiet is being expressed in some quarters about the move.
Charles Tannock, a Conservative member of the European Parliament, said the DUP - which is opposed to same-sex marriage - was a "hardline, populist, protectionist" party and a "poor fit" as a partner.
The leader of the Scottish Conservatives, Ruth Davidson, has said there are "huge disagreements" between the two parties on gay and women's rights but she does not believe this will stand in the way of Theresa May being able to govern.
Ms Davidson, who is gay and plans to marry her partner in the near future, said she had received "categoric assurance" from Mrs May about the sanctity of LGBTI rights in Scotland where - unlike Northern Ireland - equal marriage is legal in the event of any deal with the DUP.
"What is important is that we try and help, where possible, to advance these rights in Northern Ireland while making sure there is absolutely no idea of any kind of roll back here. Those are the sort of assurances I sought and received".
Speaking on Friday, the prime minister said her party had a "strong relationship" with the DUP and that she intended to form a government which could "provide certainty and lead Britain forward at this critical time for our country".
DUP will use leverage on May deal
Analysis by political correspondent Gary O'Donoghue
The clock is ticking for Theresa May. She needs to conclude a deal with the DUP in the next week or so ahead of the Queen's Speech, which will set out the new government's agenda.
That takes place on Monday 19 June - the same day Brexit negotiations are due to start.
The DUP and its 10 MPs are in a very strong position. It's all their Christmases rolled into one and they will make sure they leverage as much as they can from their advantage.
Money for Northern Ireland will undoubtedly be part of their demands, and Mrs May will expect that. But trickier will be any demands they have about the implementation of Brexit in Northern Ireland - in particular the DUP's determination to maintain a soft border with the south.
Another potential problem is the planned restart of negotiations for power-sharing in the province.
Typically the British government tries to act as an honest broker between Republicans and Unionists. But if Mrs May is doing a deal with the DUP, that could make it harder to reach an agreement with Sinn Fein.
DUP leader Arlene Foster confirmed she had spoken to Mrs May and that they would speak further to "explore how it may be possible to bring stability to this nation at this time of great challenge".
Mrs May is expected to continue assembling her top team later after she decided to keep key figures - including Chancellor Philip Hammond, Foreign Secretary Boris and Home Secretary Amber Rudd - in their current roles.
David Davis will also stay on as Brexit secretary and Sir Michael Fallon will keep his role as defence secretary.
There could be limited changes elsewhere in the cabinet while nine middle-ranking and junior ministers, including Ben Gummer and Jane Ellison, lost their seats at the general election and will need to be replaced.
Jeremy Corbyn has said Mrs May should "make way" for a government that would be "truly representative of the people of this country".
The Labour leader, who is expected to announce his shadow cabinet on Sunday, said his party was ready to form a minority government of its own, but stressed he would not enter into any "pacts or deals" with other parties.
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