The Financial Reporting Council (FRC), which regulates how firms govern themselves, is too "timid" and needs more powers, says former City minister Lord Myners.
It should "stand up to government and say we need legal change... to strengthen governance," he said.
He added that shareholders also had to take responsibility and act if a company's standards were failing.
The FRC said it had requested more powers to tackle bad behaviour.
From the end of MG Rover, to the near-collapse of Royal Bank of Scotland and HBOS, through to Tesco's accounting scandal and BHS's extinction, failings in corporate leadership have continued to stalk UK businesses.
It is 25 years since the Cadbury code was published, which put in place most of the rules governing public company practices and is overseen by the FRC.
Sir Adrian Cadbury wrote his report in 1992 following scandals such as the collapse of the bank BCCI and textile company Polly Peck, along with Robert Maxwell's raid on Mirror Group pensioners. It has been the cornerstone of corporate governance ever since.
It recommended an independent board, reasonable pay to attract executives and formal processes to appoint directors.
"The Financial Reporting Council which controls the Cadbury code, and is a rather timid body, should get stronger," Lord Myners told the BBC's Today programme.
It should "stand up to government and say we need legal change in a number of areas to strengthen governance".
The code has no punitive means of enforcement and follows a so-called comply or explain model. If a company wishes to shun a particular rule, it can give its reasons for doing so.
This arrangement aims to stop companies ducking rules as a matter course and rewards openness. But critics say it treats all rules as optional.
"It hasn't been binding enough," Lord Myners said.
In a statement to the BBC, the FRC said: "The FRC has called on the government for more powers to tackle all directors when companies fail, not just those we regulate (accountants and actuaries), and we want more scrutiny on directors fulfilling their obligations under the Companies Act.
"The Corporate Governance Code's 'comply or explain' approach has allowed the FRC to respond confidently and effectively to evolving market circumstances, which prescriptive hard rules often cannot."
Its latest monitoring report on the code shows "high compliance" among companies, but when boards don't follow the rules "too many explanations are of poor quality".
"This suggests that some boards still need to do more than pay lip service to the needs of their shareholders and other stakeholders.
"The FRC believes more focused reporting by boards on how they discharge their responsibilities is necessary and has called for more oversight powers from government to help achieve this."
Another criticism from Lord Myners is the role of shareholders themselves in controlling corporations.
"Cadbury did not focus at all on the roles and the duties and obligation of the shareholders and that's where the failing is happening," he said.
"Nobody owns enough of a company to really be put out enough to really dig in and find out what's wrong." He termed this the problem of "ownerless corporations."
This view echoed that of Chris Philp, MP for Croydon South, who told the Today programme in September that UK companies should adopt a Swedish-style shareholder committee in an effort to curb excessive pay for bosses.
The five biggest shareholders in large publicly-traded companies would sit on the committee, Mr Philp suggested, and this would make decisions on pay and hiring directors.
His plan follows a call from Prime Minister Theresa May for tighter controls on corporate excess.