LGIM, the fund arm of insurer Legal & General (>> Legal & General), which manages nearly 1 trillion pounds ($1.4 trillion) in assets, has taken a lead in improving corporate governance and its voting intentions are keenly watched, particularly by major corporations, in which it is often a leading shareholder.

In a shot across the bows for a number of companies, LGIM said it would vote against British companies where women did not represent at least a quarter of the board, and wanted a full breakdown of any gender pay gap and plans to close it.

"The vast majority of companies are making significant progress – we simply believe there is more to be done," Sacha Sadan, director of corporate governance at LGIM, said.

It also said boards should consider creating an advisory committee of external experts to help challenge consensus views.

LGIM's tougher stance was backed up by industry trade body the Investment Association, which said it had written a separate letter to 35 FTSE 350 companies that it had singled out, calling on them to improve boardroom gender diversity. They included oil giant BP and Britain's second-biggest builder Persimmon. BP and Persimmon did not immediately respond to requests for comment.

"The body of research is clear: firms with a diverse management team and pipeline make better decisions and drive innovation," the Investment Association's Chief Executive Chris Cummings said. The association's members manage nearly 7 trillion pounds in assets out of Britain.

LGIM's April 17 letter and the IA's letters, sent out between April 11 and April 16, come as annual general meetings get underway and as clients increasingly demand their investments take into account the impact on returns of environmental, social and governance-related matters.

LGIM's parent company Legal & General, has three females on its 10-member group board. In addition to diversity, LGIM said more needed to be done on climate change, long-term strategy and shareholder rights.

On climate change, LGIM said it wanted to see companies report in line with guidance from the Taskforce on Climate Related Financial Disclosures, which was set up by the G20.

"We also expect you to outline the potential impact on your business, where material, of a rise in world temperatures above the two degrees Celsius target set in the Paris climate accord," it said, referring to the 2015 deal on global warming.

Companies should also relate their strategy to the U.N.'s Sustainable Development Goals, where relevant, it said, referring to a plan to tackle a range of issues including poverty, hunger, illiteracy and disease by 2030.

Firms should also make greater efforts to demonstrate their long-term strategy was sound by showing how sustainability was reflected in their operations, through an analysis of risks and opportunities, target setting and public disclosures.

As more companies look to list with reduced shareholder rights, such as U.S. tech firm Snap did recently, LGIM said it was "increasingly concerned" and would work with regulators and others to "strengthen the integrity of the market".

($1 = 0.6982 pounds)

(Reporting by Simon Jessop; Editing by Alexander Smith and Susan Fenton)

By Simon Jessop

Stocks treated in this article : Legal & General, Persimmon, BP, Snap Inc