Ed Miliband has called for a full-scale public inquiry into banking culture and practices after the City was rocked by two major scandals in the space of a week.

The Labour leader said the industry was plagued by an “institutional corruption” that could only be eradicated by introducing a tough new code of conduct and jail sentences for immoral bankers who abused the system.

His comments were echoed by the Bank of England governor, Sir Mervyn King, who demanded a “real change in culture” as Britain’s lenders were left reeling following a week blighted by controversy.

Miliband pushed for a 12-month probe to “find out what is going on in the dark corners of the banks” after the FSA uncovered “serious failings” in the sale of complex financial products to small businesses, just days after the rate-rigging affair emerged at Barclays.

The taxpayer-backed Royal Bank of Scotland (RBS) also confirmed it was being investigated for manipulating the rates at which banks lend to each other, known as Libor.

In an interview with the Times, Miliband said: “There hasn’t been a proper reckoning for what happened in the banking crisis. The bankers told us – it’s all fine, we’ve cleaned everything up. But I’m afraid that doesn’t hold water any more.”

Calling for a systematic look at the customs and practices of the industry, he added: “We’ve got to have an open, independent inquiry with hearings to find out what is going on in the dark corners of the banks.

“Some of it clearly was illegal, but it goes well beyond that.

“There is a problem with how people operate. This isn’t just about regulation, it’s also about culture and ethics.”

Miliband said the inquiry – set up with cross-party support – would be asked to draw up a bankers’ code of conduct going beyond the “narrow” professional standards enforced by the Financial Services Authority (FSA).

Calling for the worst offenders to receive prison sentences, he added: “It should be about probity, honesty, integrity. Bankers should be struck off if they do the wrong thing … this is not a victimless crime.”

King said he believed a Leveson-style inquiry was not needed, but slammed conduct in the industry.

He said: “From excessive levels of compensation, to shoddy treatment of customers, to a deceitful manipulation of one of the most important interest rates and now news of yet another mis-selling scandal we can see we need a real change in the culture of the industry.”

He added that hard-working bank staff had been “let down” and that banks now needed “leadership of an unusually high order”.

The Financial Services Authority (FSA) revealed earlier that Barclays, HSBC, RBS and Lloyds Banking Group had agreed to pay compensation to customers who were mis-sold interest-rate hedging products.

Some 28,000 of the products have been sold since 2001 and may have been offered as protection – or to act as a hedge – against a rise in interest rates without the customer fully grasping the downside risks.

The findings come after Barclays was fined £290m by UK and US regulators for manipulating the rate at which banks lend to each other, and echoes the costly payment protection insurance (PPI) mis-selling scandal that emerged last year.

Banks are facing the threat of a criminal investigation over the fixing of the interbank lending figures that affect millions of homeowners and small firms.

The Treasury has started to look at strengthening criminal sanctions for those responsible for market abuse after the FSA exposed the dealings at Barclays on Wednesday.

Serious Fraud Office investigators are in talks with the regulator over the scandal, while pressure is mounting on the Barclays chief executive, Bob Diamond, to stand down.

Miliband described the Barclays fiasco as “the unacceptable face of capitalism”, and called on Diamond to step down.

David Cameron had said the Barclay’s chief executive had “questions to answer”, but Diamond, who was head of the bank’s investment arm at the time of the allegations, reportedly told a meeting of analysts at US bank Morgan Stanley that he would not resign.

The American banker, who waived his bonus for 2012 in light of the claims, has agreed to appear in front of the Treasury select committee to account for his bank’s actions.

HSBC and RBS are among several other lenders being investigated by the City watchdog for trying to influence the Libor and Euribor interbank lending rates to boost their profits.

Meanwhile, the RBS boss Stephen Hester waived his 2012 annual bonus following the IT fiasco that caused major problems for thousands of NatWest customers.