A banking boss’s decision to leak client details to a journalist is likely to cost the industry millions in new compliance checks as U.K. regulators prepare reviews into how banks treat people with extreme political views and whether they are subject to excessive and illegal monitoring.

NatWest’s now-former Group Chief Executive Alison Rose broke the most basic rule on confidentiality and told a BBC reporter that Nigel Farage—the U.K.’s face of Brexit and anti-immigration—had his bank account canceled because he didn’t meet the necessary wealth criteria.

Neil Hodge is a freelance business journalist and photographer based in Nottingham, United Kingdom. He writes on insurance and risk management, corporate governance, internal audit, compliance, and legal...