In a statement released early on Wednesday, NatWest Group chairman Sir Howard Davies confirmed that Dame Alison was stepping down.
It came after she said she had made a “serious error of judgment” when she discussed Mr Farage’s relationship with private bank Coutts, owned by NatWest Group, with a BBC journalist.
Sir Howard initially said the board members had decided the chief executive retained their “full confidence” but her position became ever more uncertain after the Chancellor and Downing Street were said to have “serious concerns” over her conduct.
Speaking to the PA news agency early on Wednesday, the former Ukip leader hit out at the wider NatWest Board, saying: “Anybody on that Board that backed that statement that was put out at 17.42 yesterday, a totally unsustainable and untrue statement, anybody that backed that behaviour, should be gone.”
Farage has called for a “cultural change” at the bank and within the wider industry, as he promised to continue to campaign on account closures.
He told the PA news agency he wanted a “cultural change within NatWest, they ought to go back to being a bank, rather than being a moral arbiter for political positions”.
He added: “But I think this culture runs deep through the entire banking industry. I think there is a massive anti-Brexit prejudice and I think the whole thing needs to change.”
An emergency board meeting was called late on Tuesday night to determine her future, with the announcement of her resignation coming a few hours later.
Last week, Mr Farage presented evidence, in the form of a 40-page dossier, that his account at Coutts had been closed partly due to his political views conflicting with the bank’s values.
The evidence obtained from the bank through a data request contradicted a BBC News story, which initially claimed that the account closure was motivated by commercial reasons only, citing Mr Farage’s failure to meet a £1 million borrowing requirement.
The BBC and its business editor Simon Jack apologised, saying the reporting had been based on information from a “trusted and senior source” but “turned out to be incomplete and inaccurate”.
In a statement released early on Wednesday morning, NatWest Group chairman Sir Howard Davies said: “The Board and Alison Rose have agreed, by mutual consent, that she will step down as CEO of the NatWest Group. It is a sad moment.
“She has dedicated all her working life so far to NatWest and will leave many colleagues who respect and admire her.”
In a statement of her own, Dame Alison thanked her colleagues “for all that they have done”, adding: “I remain immensely proud of the progress the bank has made in supporting people, families and business across the UK, and building the foundations for sustainable growth.
A string of Tory MPs, including former cabinet minister David Davis and Saqib Bhatti, the Conservative Party’s vice-chairman for business, had called for her resignation.
NatWest’s board of directors announced that Paul Thwaite, the current chief executive of the company’s commercial and institutional business, will take over Dame Alison’s responsibilities for an initial period of 12 months, pending regulatory approval.
The board said in a statement that a further process to appoint a permanent successor will take place “in due course”.
City minister Andrew Griffith will meet Britain’s largest banks on Wednesday morning to address concerns related to customers’ “lawful freedom of expression”.
He said it was “right” that Dame Alison had stepped down.
“This would never have happened if NatWest had not taken it upon itself to withdraw a bank account due to someone’s lawful political views. That was and is always unacceptable.
“I hope the whole financial sector learns from this incident. Its role is to serve customers well and fairly – not to tell them how or what to think.”
Mr Farage said that the “next step” is to support the changes introduced by Mr Griffith.
“He has been very clear in his statement this morning that banks should not be closing people down on the basis of their opinions.
“But the entire industry needs to wake up to the absolutely appalling way it has been treating people all over the country.
“We bailed these people out and in return they close our branches, they close our personal and business accounts on a huge scale. We need real change here and I am going to go on pushing for it.”