LONDON — The British authorities are investigating Barclays and its chief executive, James E. Staley, after he admitted to trying to learn the identity of a whistle-blower last year, the bank said on Monday.

The investigation adds to the public relations troubles of the bank, whose reputation has been hit hard in Britain in recent years by revelations of employee misconduct dating from the financial crisis and earlier.

The lender announced in February that it would end its restructuring plan this year, an important step in efforts to turn the bank around. Resolving litigation and inquiries of possible misconduct have been an important part of that plan.

On Monday, the bank said that it would formally reprimand Mr. Staley and make a “very significant compensation adjustment” to his bonus after the Prudential Regulation Authority and the Financial Conduct Authority finish their inquiries.

“I am personally very disappointed and apologetic that this situation has occurred, particularly as we strive to operate to the highest possible ethical standards,” John McFarlane, the Barclays chairman, said in a news release. “The board takes Barclays culture and the integrity of its controls extremely seriously. We have investigated this matter fully using an external law firm, and we will be commissioning an independent review of Barclays processes and controls to determine what improvements may be required.”

Barclays said the company and Mr. Staley would cooperate with investigators.

Mr. Staley, a former top executive of JPMorgan’s investment bank, became chief executive in December 2015, replacing Antony Jenkins.

Mr. Jenkins had aggressively sought to reshape the lender’s corporate culture after a scandal involving the manipulation of the London interbank offered rate, a benchmark interest rate known as Libor.

Barclays agreed in 2012 to pay $450 million to resolve accusations that it had tried to manipulate rates, becoming the first bank to reach a settlement in the Libor investigation. The scandal cost Robert E. Diamond Jr., the chief executive at the time, his job.

Mr. Jenkins was praised for his efforts to change the bank’s culture, but he was ousted in July 2015 after directors lost confidence in his ability to improve returns for shareholders.

On Monday, the bank said that its board had learned early this year of Mr. Staley’s attempt to identify the author of an anonymous letter, and that it had hired the law firm Simmons & Simmons to investigate the matter. The bank also said it also “promptly notified” the Financial Conduct Authority, the Prudential Regulation Authority and other relevant agencies.

In June 2016, anonymous letters were sent to the Barclays board and to a senior executive raising concerns about a senior employee who had been recruited by the lender that year, the bank said.

“Amongst other issues, the letters raised concerns of a personal nature about the senior employee, Mr. Staley’s knowledge of and role in dealing with those issues at a previous employer, and the appropriateness of the recruitment process followed on this occasion by Barclays,” the bank said.

The law firm’s investigation found that Mr. Staley had asked the Barclays information security team to try to learn the identity of the author of one of the letters because he considered “the letters were an unfair personal attack on the senior employee.”

He was told at the time that doing so was not appropriate, as both letters were logged as letters from whistle-blowers. No further action was taken at the time.

But Mr. Staley inquired in July 2016 whether the whistle-blowing issue had been resolved.

He “honestly, but mistakenly, believed” that it was permissible to identify the author of one of the letters, the bank said, citing the law firm inquiry.

Mr. Staley then asked the bank’s information security team to try to identify the author of one of the letters and sought the assistance of a United States law enforcement agency in doing so. The information security team was ultimately unsuccessful in identifying the authors, and no further steps were taken, the bank said.

“I have apologized to the Barclays board, and accepted its conclusion that my personal actions in this matter were errors on my part,” Mr. Staley said in a statement. “I will also accept whatever sanction it deems appropriate. I will cooperate fully with the Financial Conduct Authority and the Prudential Regulatory Authority, which are now both examining this matter.

“Our whistle-blowing process is one of the most important means by which we protect our culture and values at Barclays,” he continued, “and I certainly want to ensure that all colleagues, and others who may utilize it, understand the criticality which I attach to it.”