Coutts, the Queen's bank, could end up paying compensation to thousands of customers after admitting that some may have been given unsuitable investment advice.
The private bank and wealth manager, founded more than 300 years ago, said it was reviewing customer files going back as far as 1957, and added that "if clients have suffered any financial detriment, they will be compensated in full".
The bank, part of the Royal Bank of Scotland group, said it had agreed with the Financial Conduct Authority (FCA) that it would conduct a review of the suitability of investment advice given in the UK.
Coutts and Co chief executive, Michael Morley, said: "Looking back, there have been some instances where the advice given during our previous advice process could have been better, and we are working hard to address that. We want our clients to be absolutely certain that every investment made by them is indeed suitable, and continues to be suitable."
The bank said the review of all of its clients' investments would take some months and was unlikely to be concluded until early 2015. It will be checking the suitability of the historic advice provided to customers.
Coutts, which was founded in 1692, said that while it was confident the advice given to clients today was suitable and "in line with the highest standards in the industry," it operated different systems prior to 2012.
"A large part of our previous weakness lay in our record-keeping, much of which was paper-based," it said, adding that its front-line staff had previously carried out two "complex" roles simultaneously: general banking and wealth management advice.
The review is focusing on investments held on 26 November 2012 and does not include non-advised – or "execution-only" – transactions. The bank said it had agreed with the FCA that customers who left Coutts before that date were not within the scope of the investigation, but added: "If a past client wants to complain, they can do so."
It said the final cost of redress and potential individual compensation amounts were unknown at this time.
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