It comes after Mr Farage revealed last month the bank - which is owned by NatWest Group - had written to inform him that his personal and business accounts were being shut down without explanation.

The BBC then reported it was because the former UKIP and Brexit Party leader had fallen below the level of wealth required by the bank, and that his political opinions were not a factor in the decision.

But Mr Farage then obtained a 40-page dossier from Coutts which suggested the move was taken partly because his views did not align with the firm's "values", including his position on LGBTQ+ rights and friendship with former US president Donald Trump.

In a statement, the broadcaster said: "Because of this evidence, we have since changed the headline and the copy on the original online article about his bank account being shut for falling below the wealth limit to reflect that the claim came from a source and added an update to recognise the story had changed.

"We acknowledge that the information we reported - that Coutts' decision on Mr Farage's account did not involve considerations about his political views - turned out not to be accurate and have apologised to Mr Farage."

The corporation's business editor, Simon Jack, also said sorry in a tweet.

He wrote: "The information on which we based our reporting on Nigel Farage and his bank accounts came from a trusted and senior source. However the information turned out to be incomplete and inaccurate.

"Therefore I would like to apologise to Mr Farage."

Last week, NatWest's CEO Alison Rose apologised to Mr Farage for the "deeply inappropriate comments" made about him in documents prepared for the company's wealth committee.

She said the remarks "did not reflect the view of the bank", which has now offered him "alternative banking arrangements".

Read more:
Key points from Coutts' dossier on Nigel Farage
Are banks allowed to close accounts?

In a video posted on Twitter, Mr Farage thanked Mr Jack and BBC News head Deborah Turness for saying sorry, and said he would take some time to "absorb" it.

He added: "It's not often the BBC apologise."

Over the weekend, Mr Farage said his lawyers had written to the Information Commissioner's Office (ICO) to ask them to investigate.

In the letter, he accused the NatWest Group of mishandling his personal data and of handing over personal information to the BBC.

The row prompted the Treasury to announce reforms designed to better protect customers from similar closures in future.

New measures include making banks explain why they are shutting an account, and extending the notice period from 30 days to 90 days.

City Minister Andrew Griffith has also summoned bank and building society bosses for talks, and warned them the government will "take all action necessary" to crack down on accounts being closed in response to customers' political views.