Sky News has learnt that directors of the taxpayer-backed lender were locked in discussions, with sources saying Dame Alison was almost certain to step down in the wake of briefings by Downing Street that she had lost the confidence of the prime minister and chancellor.

One insider cautioned, however, that a final decision had yet to be taken, while NatWest, which is 39%-owned by British taxpayers, declined to comment.

Dame Alison's departure would cause huge embarrassment to the NatWest board, which just hours earlier had issued a statement saying it "retains full confidence in Ms Rose as CEO of the bank".

If confirmed, it would also bring an abrupt and premature end to the executive career of the only woman to run one of Britain's biggest high street banks.

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A statement could come within hours, but is likely before the stock market opens on Wednesday morning, a source said.

Dame Alison has been embroiled for the last ten days in an intensifying row over the disclosure of inaccurate information to BBC business editor Simon Jack, about the decision to close Mr Farage's accounts with Coutts, a NatWest subsidiary.

Mr Farage has accused the bank's management of a "serious breach", calling for Dame Alison's dismissal.

He told Sky News: "I think her position is totally untenable. Anybody, even a junior clerk in the bank, if they breached the confidence of a customer would have to go... I don't believe for a moment she will be there by the end of Friday."

His call was echoed by Tory former cabinet minister David Davis, who said Dame Alison had "little choice but to resign".

The former UKIP leader extracted apologies from both the NatWest chief executive and the BBC over the affair, with Dame Alison acknowledging on Tuesday that she had been responsible for the erroneous briefing that his accounts had been terminated purely for commercial reasons.

The Times reported on Tuesday night that Downing Street and the Treasury were keen for Dame Alison to step down.

NatWest said it would "commission an independent review into the account closure arrangement at Coutts, and the lessons to be learnt from this", with the City watchdog demanding an inquiry into the breaches of client confidentiality.

Dame Alison said earlier: "I would like to say sorry to the Board and my colleagues.

"I started my career working for National Westminster Bank.

"It is an institution I care about enormously and have always been proud to be a part of. It has been the privilege of my career to lead the bank and I am grateful to the Board for entrusting me with this role.

"It is therefore all the more regrettable that my actions have compounded an already difficult issue for the Group."