Vince Cable has urged shareholders in UK banks to rise up and purge their companies of corrupt executives, who he says have allowed "systemic abuse" to take root in the banking system.

The business secretary, writing in the Observer, says it is now clear that no one at Barclays Capital, the investment bank that triggered the market-rigging scandal, is prepared to take responsibility for endemic corruption, so the ultimate owners of banks must take matters into their own hands.

Describing the problems in UK banking as "a moral quagmire of almost biblical proportions", Cable says the government is taking urgent action, including creating a clearer separation between "casino-style investment banking" and retail banking on the high street. Ministers will this week begin a review into the Libor system under which banks lend to each other and Cable hints that US-style criminal sanctions, such as the threat of prison terms, could be considered against those who abuse it.

But he says shareholder power will be crucial. "Regulators are a backstop: they don't own banks," he writes. "The governance at the top of our leading banks has been shown to be lamentably weak. No one at the top of Barclays will take responsibility for systemic abuse.

"Shareholders, the owners, have a major responsibility here. I am bringing in legislation to strengthen their control over pay and bonuses, through binding votes, but shareholders have to get a stronger grip on weak boards and out-of-control executives."

Shareholders have already opposed the pay package of Sir Martin Sorrell, the head of advertising giant WPP, while Trinity Mirror boss Sly Bailey and Aviva's chief executive Andrew Moss quit following opposition from investors. Cable says he is determined to encourage "cultural change" throughout the system. He cites the takeover by the not-for-profit Co-operative Bank of a large chunk of the Lloyds bank network as a model for a future system.

It was announced on Saturday that the Barclays chief executive Bob Diamond, who has faced calls from Labour to quit, will be summoned for questioning in front of the Commons Treasury select committee on Wednesday to explain the £290m fine imposed by US and UK regulators on Barclays Capital for rigging a key interbank lending rate.

Non-executives, including chairman Marcus Agius, will appear on Thursday. "The Libor interest rate benchmark – crucial to transactions right across the economy and affecting millions of people – was systematically rigged over a period of years," said the committee's chairman, Andrew Tyrie. "This is the most damaging scam I can recall. The reputation of Britain's financial services industry has been severely tarnished, albeit unfairly for the overwhelming majority unconnected with the scam. The public's trust in banks has been even further eroded. Restoring the reputational damage must begin immediately."

There are signs that Agius could be replaced to address demands for the bank to demonstrate accountability at the top. But it is far from clear that the idea has the support of the bank's board. If such a plan were implemented, one option might be for Agius to be replaced temporarily by the former top accountant Sir Michael Rake, who holds a key role as the "senior independent director". Barclays issued a statement on Saturday saying it was "categorically wrong" to suggest Agius had plans to step down.

Ed Miliband – in a speech to the Fabian Society on Saturday – attacked the government's failure to launch a public inquiry. "I have news for David Cameron: the people want a moment of reckoning for our banks," he said. "The British people will not tolerate the establishment closing ranks, saying we don't need an inquiry. They want a light shone into every dark corner of our banking system. They want bankers held to account."

Meanwhile, legal action being brought across the Atlantic suggests the scandal is spreading. A lawsuit filed by the US stockbroking firm Charles Schwab alleges that Barclays was one of 16 banks whose manipulation of interbank lending rates "artificially depressed the value of tens of billions of dollars" in funds held by investors. It alleges the defendants, which include Lloyds, HSBC and RBS, "knowingly colluded" to keep the rates low and "engaged in a media strategy" to deflect attention from their actions. The banks are contesting the allegations.

An affidavit filed by the Canadian Competition Bureau last year reveals that investigators are examining allegations that traders at a number of banks, including the Canadian arms of RBS and HSBC, colluded to set interest rates. The claims are denied by the banks.

With investigations in the EU, the US, Switzerland, Singapore and Japan, the scandal is threatening to go global. Sources suggested hedge funds and brokers could be drawn into the affair.

Cable's call for US-style penalties could see those found guilty of white-collar fraud serve long stints in jail. Bernie Ebbers, the boss of the collapsed US telecom giant WorldCom, was sentenced to a minimum 25 years in prison for his part in defrauding investors.

• This article was amended on 3 July 2012 to remove a reference to Tesco.