The U.K.’s Financial Reporting Council levied a total of £5.05 million ($6.1 million) in fines against KPMG LLP and one of its partners for failings related to regulatory reports the firm created and submitted on behalf of Bank of New York Mellon Corp. entities, the latest action by the regulator against the Big Four accounting firm.

KPMG, the auditor of BNY Mellon entities Bank of New York Mellon London Branch and Bank of New York International Ltd., and KPMG partner Richard Hinton admitted misconduct in preparing and submitting reports on BNY Mellon’s compliance with regulatory requirements in 2011, the FRC said.

The reports were submitted to the Financial Services Authority, a former regulator for the financial services industry that was replaced by the Financial Conduct Authority and the Prudential Regulation Authority in 2013, according to the FRC.

The regulation at the center of the KPMG case, the client assets sourcebook, or CASS, involved BNY Mellon’s role as a custodian of client assets valued at their peak at more than £1 trillion. KPMG’s work didn’t meet certain regulatory standards, the FRC said.

“The misconduct consisted of a failure to understand and to apply fundamental rules of CASS,” an FRC tribunal said in a statement. KPMG didn’t ensure appropriate training, support and supervision of the 2011 audits of the bank’s client assets sourcebook, according to the regulator.

The FRC, which oversees audit and accounting firms in the U.K., fined KPMG £5 million and issued a reprimand. The fine was discounted to £3.5 million because the firm admitted misconduct, the regulator said. Mr. Hinton received a discounted fine of £52,000 and a reprimand.

“We regret that aspects of our work did not meet the standards expected by our regulator,” KPMG said in a statement. BNY Mellon declined to comment.

The FRC imposed a requirement for KPMG to conduct a quality performance review of each employee signing a client assets sourcebook, and to provide details about the outcome of the reviews. The review process will last for three years, the regulator said.

Thursday’s fine comes amid increased scrutiny over the quality of work provided by KPMG and other professional services firms in the U.K., including the three other Big Four companies: Deloitte LLP, Ernst & Young LLP and PricewaterhouseCoopers LLP.

The FRC, which punished KPMG for other audit-related cases earlier this year, is conducting a review of the conduct and the governance of the firm’s audit unit in the U.K.

It is also investigating KPMG’s audits of financial statements of Carillion PLC, a U.K. construction company that collapsed last year.

Carillion’s failure triggered an intense debate about the state of the U.K. audit industry. Regulators and lawmakers have proposed substantial changes to the structure of the sector, including a suggestion to break up the Big Four.

As part of the changes introduced by the U.K. government, the FRC will become part of a new regulatory body called the Audit, Reporting and Governance Authority.

Write to Nina Trentmann at Nina.Trentmann@wsj.com