As he arrived at the Home Office to take up new his job earlier in the day, Mr Javid vowed to make sure people caught up in the Windrush scandal are treated with “decency and fairness”.
Ms Rudd became the fifth departure from the cabinet since last year’s snap general election after admitting she had “inadvertently” misled MPs over the existence of targets for removing illegal immigrants.
The MP for Hastings and Rye stepped down on Sunday evening, a day before she was due to make a statement in the House of Commons on the targets and illegal migration, as she faced increasing pressure over the handling of the Windrush fiasco.
Good morning and welcome to The Independent's live blog covering Amber Rudd's resignation.
Theresa May will be forced into making another cabinet reshuffle after the home secretary resigned yesterday evening.
Amber Rudd resigns as home secretary, Downing Street saysAmber Rudd has resigned as home secretary following growing pressure over the Home Office’s use of deportation targets for immigrants and the wider Windrush scandal. The cabinet minister finally quit on Sunday after yet another leaked document cast doubt on her claims that she was unaware of targets her officers were using in throwing increasing numbers of people out of the country.
Diane Abbott, the shadow home secretary, has said Theresa May must face MPs following Amber Rudd's resignation.
The prime minister must answer questions in the Commons about her knowledge of migrant removal targets, the Labour frontbencher said.
She told BBC Radio 4's Today programme: "We want to talk to her about the aspects of the so-called hostile environment which she was responsible for and led to the Windrush fiasco."
Ms Abbott added: "I brought it to the House last week because there was this difficulty and problem about understanding her evidence to the Home Affairs select committee.
"But fundamentally the reason she had to resign was because of the Windrush fiasco.
"Somebody had to take responsibility. It happened on her watch, therefore I think it is right that she resigned."
Amber Rudd’s resignation letter in full and the Prime Minister’s responseAmber Rudd has resigned as home secretary amid increasing pressure over the way the Home Office handled immigration policy. Her resignation came after leaked documents undermined her claims she was unaware of the deportation targets her officers were using.
Damian Green, who was sacked as first secretary of state in December after making "misleading" statements about allegations police found pornography on computers in his parliamentary office in 2008 which breached the ministerial code, has said Ms Rudd was right to quit.
The former immigration minister said he did not know during his time in the Home Office about the destruction of the landing cards of Windrush migrants.
He told Today: "I'd never known about the landing cards at all. That's the sort of thing that happens in departments."
Mr Green said he was told about the phrase "hostile environment" in relation to illegal immigrants.
"That was just a Home Office policy which we inherited," he added.
Mr Green said Ms Rudd, who has been a key Remainer in the Cabinet, would speak "freely" now she has left government.
He said: "I'm sure that Amber will speak freely on all matters from the backbenches."
Asked if she would use her inside knowledge to inform the debate, he replied: "I'm sure she will."
Damian Hinds, the education secretary, said he hopes Ms Rudd "will be back".
He told Today: "I very much regret that Amber has taken the decision to resign but I understand why she has done so."
Who could replace Amber Rudd as home secretary?Amber Rudd has handed in her resignation to the Prime Minister, and created a vacancy in one of the most powerful positions in British politics. The Windrush fiasco is still in the spotlight, and Ms May will need someone who can pick up the baton swiftly and restore calm to an increasingly frustrated public. With the Brexit negotiations ongoing, the prime minister will also be looking for a home secretary who can help with the balance of power between Leave and Remain cabinet members. Michael Gove
The transport secretary, Chris Grayling, said the string of cabinet losses in recent months was "unwanted noise".
He told Today: "We have had some unwanted noise in the last few months, some unwanted loss of parliamentary colleagues and Cabinet colleagues.
"None of that are things we would have wanted to happen. They happen to all governments to some degree at some point or another.
"None of us want to lose parliamentary colleagues but the truth is we have got a wealth of skill in the Conservative Parliamentary party."
Asked if he was going to be made the new Home Secretary, Mr Grayling said: "I have absolutely no idea at this moment in time who the prime minister will appoint as the new home secretary."
Mr Grayling, a Leave supporter, suggested Ms Rudd did not need to be replaced by another Remainer.
"We are now a government that is united in wanting to deliver the best outcome for Britain in Brexit," he said.
"Okay, we have some debates and discussions about how we get there.
"But I think what's most important is she gives the right person this job because it is much more than the Brexit negotiations. It's about security and it's about the safety of our citizens."
Mr Grayling said Ms Rudd had "made a mistake" because she had not been "fully aware" of what was happening on the ground.
"She's come to the view that she should have known more, that she didn't and she's got to take responsibility for that," he said.
Mr Grayling said Ms Rudd would "never deliberately" mislead Parliament.
Labour's Stephen Doughty, a member of the Home Affairs select committee, said he did not know if Ms Rudd had inadvertently misled MPs.
He told Today: "She clearly misled us and we don't know her reasons for doing so."
Asked if he believed that Mrs May had known that Ms Rudd's comments to the committee were wrong at the time, he replied: "I do suspect that Theresa May knew."
Mr Doughty said there had been a string of problems in the Home Office under Ms Rudd about people being wrongly challenged about their nationality or facing deportation.
He said: "Quite frankly, how she didn't know there was a problem in her department is quite extraordinary."
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