The warning follows last year's admission by Lloyd's of London [SOLYD.UL] of sexual harassment and daytime drinking in the market, which employs nearly 50,000 people. Lloyd's has introduced a plan to raise standards.

"A senior manager's failure to take reasonable steps to address non-financial misconduct could lead us to determine that they are not fit and proper," Jonathan Davidson, the Financial Conduct Authority's Executive Director of Supervision, Retail and Authorisations said in a letter on Monday.

Senior manager approval is based on a number of factors including integrity and reputation, the FCA said in the letter to chief executives, which was also posted on its website.

"Although work has been undertaken in the market to tackle the issue of non-financial misconduct, it continues to be prevalent and will be a key focus for our supervision of firms and of senior managers," Davidson said.

Firms should share the letter with senior executives and boards, and "act promptly" to address shortcomings, he added.

The FCA did not name the companies it had written to.

Other insurers are also taking steps to improve conduct after the Lloyd's case. AXA this week said it has started management training for brokers, working with the Brokerbility Academy, including advice on preventing and tackling bullying and sexual harassment.

(Reporting by Carolyn Cohn; Editing by Alexander Smith)