Britain’s fund managers have written to the top 350 public companies telling them to publish how much their chief executives make compared with the average employee and to justify the amounts paid out each year.

The Investment Association, which represents £5.7tn in funds, said it had toughened up its guidelines for companies because of growing unease about the sums earned by chief executives. Theresa May has promised to rein in runaway pay for bosses that she says has left ordinary workers behind.

In its letter to remuneration committee chairmen, the association warned that the current political and economic climate meant pay would receive a lot of attention at next year’s annual general meetings.

The association called on companies to publish the ratio of chief executive pay to that of the median employee and also between the chief executive and the executive team to help shareholders judge whether the payments were fair. It also told companies to explain properly why the amount paid to the chief executive was justified each year instead of referring to pay schemes set down beforehand.

The more demanding guidelines follow a heated series of AGMs that featured defeats and bruising protests over pay at some of Britain’s biggest companies. BP shareholders voted against the £14m award for Bob Dudley, the oil company’s chief executive, for a year in which it reported record losses, cut thousands of jobs and froze employees’ pay.

There were also heavy votes against pay at WPP, where Sir Martin Sorrell received more than £70m, and at other companies such as Weir and Smith & Nephew. At next year’s AGMs, shareholders will cast binding votes on pay reports that every three years set out how bosses will be paid.

The leaders of Britain’s public companies earned an average £5.5m each last year – a 10% increase – and typically earn 129 times more than their employees, according to the High Pay Centre thinktank. No FTSE 100 company yet publishes the chief executive-to-employee pay ratio.

Andrew Ninian, the association’s director of corporate governance, said: “Issues surrounding executive pay are a growing concern for investors, politicians and society as a whole. The Investment Association and its members felt that it was vital to rebuild trust and update our principles to ensure that we are not only acting as responsible stewards for our clients but also show that we are aligned with the current climate.”

The association made changes to its guidelines to reflect the recommendations of a working group that reported in July. Like the group of City grandees, the association stopped short of calling for binding annual votes on pay, as proposed by Theresa May in her attack on corporate excess when campaigning for the Tory leadership.

Ninian said changes to the association’s principles were separate from proposals for binding votes, which are the subject of political discussion. He said investors would wait to see the government’s proposals before taking a position on binding pay votes.

He said overly complex pay plans had helped fuel big rises because investors had trouble understanding them. The association told companies to simplify pay structures and to publish the terms alongside the resulting pay figures so shareholders could see how they worked.

Tony Pidgley, founder and chairman of Berkeley Homes, was paid £21.5m in 2015. Photograph: David Levene/The Guardian

The association also asked companies to consider alternatives to long-term incentive plans that have paid out huge sums to some chief executives. WPP has said it is drawing up a new pay plan for Sorrell after the previous one gave him one of the biggest paydays in UK corporate history. In another example of big payouts under existing schemes, Berkeley Homes paid founder and chairman Tony Pidgley £21.5m last year thanks to share options granted in 2009.

Ninian said: “The increasing complexity of remuneration structures has been the driving force behind these issues. It is vital that companies have the opportunity to choose the right structure for their business and this must be done in close partnership with their shareholders.”

Shareholders are under pressure to take a tough line with companies over pay. The Institute of Directors, an employers’ lobby group, has said soaring pay at the top threatens to undermine capitalism and could bring unwanted government interference if companies do not put their own houses in order.

Ninian said: “We look forward to working with the government as it puts together its own corporate governance agenda.”

• This article was amended on 1 November 2016. There was a vote against boardroom pay at Smith & Nephew, not Smiths Group, as previously reported.