The chief executive of NatWest Group has apologised to Nigel Farage for the closure of his bank accounts and ordered an immediate review of the processes followed by its Coutts subsidiary.

In a letter to Mr Farage seen by Sky News, Dame Alison Rose said she regretted “deeply inappropriate comments” about the former UKIP leader in internal bank documents.

The bank chief, whose employer is backed by UK taxpayers, said it had offered Mr Farage “alternative banking arrangements”.

“I fully understand yours and the public’s concerns that the processes for bank account closures are not sufficiently transparent,” she wrote.

“Customers have a right to expect their bank to make consistent decisions against publicly available criteria and those decisions should be communicated clearly and openly with them, within the constraints imposed by the law.”

NatWest’s climbdown is likely to be seen as a humiliating episode for Dame Alison, whose company had previously sought to shut down the row with Mr Farage by saying it was limited by client confidentiality rules.

Her letter was timed to coincide with the publication of reforms by the Treasury, confirming a report earlier this week by Sky News.

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Wednesday: Coutts responds to Farage claims

The new rules will force banks to give customers 90 days’ notice of account closures and to provide an explicit explanation of the reasons for the decision.

Rose said a review of Coutts’ processes would report to her, adding: “I believe very strongly that freedom of expression and access to banking are fundamental to our society.”

Mr Farage had become embroiled in a public fight with the bank about whether his accounts had been closed for commercial reasons – as NatWest had appeared to brief unofficially – or whether it was because of his political views.