By Elizabeth Piper

LONDON (Reuters) - Britain will unveil proposals on Tuesday to encourage better corporate behavior, part of Prime Minister Theresa May's drive to support the millions of people she says voted for Brexit in protest at 'out of touch' elites.

Her plans to have workers represented on company boards have already been watered down, however, with business minister Greg Clark saying on Tuesday the government would not "overturn" Britain's successful system of having unitary boards.

The government says it wants to stop "an irresponsible minority of privately-held companies acting carelessly - leaving employees, customers and pension fund beneficiaries to suffer when things go wrong". But its Green Paper, or consultative document, is likely to raise more questions than it answers.

May, who faces some of the trickiest negotiations since World War Two over Britain's divorce with the European Union, has pledged to look after people who are 'just about managing'. She has said she will narrow the gap between workers and company bosses by tackling excessive executive pay.

"We will explore ways to improve and extend good governance across big business so that everybody plays by the same rules and we create an economy that works for everyone, not just the privileged few," May said in a statement.

She did not name any companies, but British lawmakers have backed stripping billionaire Philip Green of his knighthood over the collapse of the BHS department store, which went into administration in April.

The proposals will look at ways to ensure that employees, customers and other stakeholders are better represented in the boardroom and that executive pay packages reflect company performance, the government said in a statement.

They will also include a demand that the largest private firms comply with "a bespoke code of practice" or explain in their annual accounts why they haven't, and make privately-held businesses report more consistently on diversity, greenhouse gas emissions and social and community issues.

The proposals will be discussed by a wide range of interested parties before a White Paper is published setting out the government's proposals for future legislation. This may also be consulted on before a formal bill is presented to parliament.

While describing the proposals as "a big change", Clark, who will deliver the Green Paper to parliament, said the government would not aim to "overturn" the tradition of company directors not necessarily being the delegates of certain groups.

Saying companies could have workers represented on boards, he said: "It is available for companies ... we're not going to make it happen. But I think what we do want to do is to give a stronger voice to workers on boards."

On executive pay, he said the government will propose ways of curbing excessive rates, including considering whether there should be an annual binding vote by shareholders.

"I want them (CEOs) to be paid in line with performance and one of the concerning aspects is not just has pay increased at the top ... but actually it has substantially outpaced the performance of the underlying shares," he said.

"We do want to see the stewards of our investment, through pension funds, taking an active role in requiring not just the level of pay but the structure."

(Additional reporting by Kylie MacLellan and William James; Editing by Michael Holden and Catherine Evans)