Britain's leading retail banks are still failing a quarter of their customers when advising them on investment products, financial regulators said Wednesday.

Despite years of investigations, billions of pounds in compensation for past scandals and repeat apologies from senior executives, the industry is still providing unsuitable advice or failing to make adequate background checks on customers in 26% of cases.

The Financial Services Authority has begun a formal investigation into one bank. It declined to comment on the identity of the bank but several media reports named Santander UK, part of Spain's biggest banking company, as the target.

Santander declined to comment on whether it was the subject of an investigation. But it said it was "considering the findings" of the review in the context of measures it took last year to prepare for the introduction of new FSA rules, including extra training for staff and new risk questionnaires.

"We continue to believe it is important to offer customers access to a broad range of financial products which are suitable to their needs and individual situations, and we are working towards that objective," Santander said in a statement.

Between March and September 2012, the FSA covertly sent investigators to six major retail banks to review their advice, an exercise known as "mystery shopping." In 11% of the 231 cases, the advice given was unsuitable and in a further 15% of the cases, advisers did not gather enough information to be able to judge whether the product offered was appropriate or not. No products were sold as a consequence of the exercise.

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Clive Adamson, head of supervision at the FSA, said he was disappointed with the results of the review but encouraged by the action the firms have taken since to put things right for customers.

"This review shows that customers are not consistently getting the quality of advice on their investments that they should expect when visiting an adviser in a bank or building society," he said in a statement.

The British banking industry is struggling to repair its reputation after a series of scandals that have undermined public trust, strained balance sheets and prompted commitments of a change in course by leading players.

Barclays, which set aside £2.45 billion last year to compensate the victims of improper selling scandals, unveiled an overhaul Tuesday aimed at providing a fresh start for one of the oldest names on the High Street.

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Banking lobby group BBA said the FSA review showed the majority of clients received good advice, but acknowledged more needed to be done.

"Any examples of advisers failing to gather enough information on their customers and not recommending the right products are unacceptable," it said in a statement.

The mystery shopping exercise took place before the introduction of the new FSA rules requiring all advisers to gain an extra qualification and ending commission payments, removing the incentive for them to push products that paid the highest commission.

"We would therefore expect the next FSA mystery shopping review to show real improvements," the BBA said.