The FRC suggests a review of non-executive directors' independence
Company chairmen and boards could face an annual shareholder vote to stay in their job, under new proposals.
The Financial Reporting Council's (FRC) proposals on business governance follow Sir David Walker's review of banks last week.
Under the current FRC code of practice, board members must face re-election at least once every three years.
The Association of British Insurers said consideration should be given to re-electing all board members annually.
Sir Christopher Hogg, FRC chairman, said board members must "think deeply" about their responsibilities.
The main proposals also include:
• That the leadership of the chairman, the roles, skills and independence of the non-executive directors and their level of time commitment should be reviewed
• Boards should be evaluated externally at least every three years and the chairman should hold regular development reviews with each director
• That performance-related pay should be aligned to the long-term interests of the company and its policy on risk.
Sir Christopher said that although the review found no evidence of serious failings outside the banking sector, sensible improvements to the code would benefit governance across all businesses.
"The principal lesson of the financial crisis is that those on boards must think deeply about their individual and collective roles and responsibilities," he said.
"The chairman has a vital role to play in ensuring that the executives have appropriate freedom to manage the business but also accept the importance of opening themselves to challenge and earning the trust of the whole board."
Sir Christopher also stressed the importance of boards following the spirit of the code, rather than just its details.
"The FRC will probably be applauded for trying to shift the balance of boards' responsibilities from box-ticking and formal compliance to a proper appreciation of their responsibilities as the custodians of the wealth-generating machines," said the BBC's business editor, Robert Peston.
The FRC will now consult on its proposals until March next year.
It said it could not enforce the recommendations outlined in the review, but would rely on shareholders to push through change.
The Association of British Insurers said re-electing just the chairmen every year could be "too blunt an instrument".
"We will talk to our members about whether they would prefer annual re-election of all directors, and will respond to the consultation in due course," the ABI said.
In a separate review last week of banking boards, Sir David Walker said that financial institutions should be forced to publicly disclose the number of their employees who earn more than £1m a year.
Sir David also concluded non-executive directors needed more power to monitor banks' risk taking and pay deals.