The government will ban the bosses of failed banks from working in the financial industry, the chairman of the City regulator has said.

Lord Turner, chairman of the Financial Services Authority (FSA), who has been calling for tougher regulation in the City, said he understood that George Osborne would accept his proposal that the directors of failed banks be automatically banned or stripped of their pay. This was one of Turner's recommendations in the FSA's report into what went wrong at Royal Bank of Scotland (RBS).

Osborne has said he will respond to the report this week. He told MPs the government "will be publishing a consultation in response to the report on the failure of RBS and will consider the possibility of criminal sanctions for directors of failed banks where there is proven criminal negligence".

Over the weekend, the prime minister ordered an investigation into the way the key interest rates are set which led to the record £290m fine being levelled on Barclays last week.

Turner said regulation in the City needed to be tightened considerably. He rejected suggestions that the last Labour government had done nothing to toughen the regulatory regime in the City, but said there was a need to go much further.

"If you go back over 20 years, we started with, in these sort of areas, a very light touch, self-regulatory approach. And slowly over the last 15 years or so we have toughened our approach," Turner said on the BBC's Andrew Marr Show.

Under Labour the FSA was given the power to bring criminal charges in relation to certain areas of market abuse, he said. But these did not cover the interest rate market which Barclays attempted to manipulate, according to regulators who handed the bank a record £290m fine last week.

Marcus Agius, chairman of Barclays, is expected to step down on Monday after the fine – the FSA portion of which was £59.5m, the rest being levied by US regulators, the Department of Justice and Commodities Futures Trading Commission.

Turner said: "I think we now have to look further and see whether we should strengthen these powers considerably on top of what we have now got at the moment."

The calls for a criminal investigation – most likely led by the Serious Fraud Office – continued unabated when Vince Cable, the business secretary, urged a criminal investigation into the Barclays traders involved in the interest-rate setting scandal. The 14 traders were found to have attempted to manipulate two key benchmark interest rates – the London interbank offered rate (Libor) and Euribor, its European equivalent – which are used to help set the prices at which households and businesses borrow. Cable said the public would not understand why people were jailed for petty theft while bankers were getting off "having perpetrated what looks like conspiracy".

And he said he agreed with Lord Blair, the former Metropolitan police commissioner, who said there appeared to be evidence that Barclays employees were engaged in conspiracy to defraud.

In an interview with Sky's Dermot Murnaghan, Blair said: "There have to be police inquiries into this. Anybody, the youngest detective, would say this is conspiracy to defraud. It can mean nothing else. And therefore someone has to launch a criminal inquiry into this behaviour."

Cable said "his instincts" were to agree with Blair.

The SFO repeated earlier statements that it was "aware of the matters under investigation and there are ongoing discussions between the FSA and the SFO about the evidence as it develops".

As many as 20 other banks are thought to be under investigation. RBS, for instance, sacked four traders last year in connection to the ongoing regulatory action.

But Labour said that, for all the coalition's talk of cracking down on the City, recent experience suggested that minsters did not have the will to face down bankers on issues of key importance.

In a speech at the weekend, Ed Miliband said this was illustrated by the government's announcement last month that it was not going to implement in full the recommendations of the Vickers report on the need to separate investment banking from retail banking.

Miliband said Vickers wanted the sale of interest rate insurance – which was at the heart of a mis-selling scandal exposed by the FSA last week – to be classified as an investment banking activity, not a high street banking one. But the government rejected this recommendation after the banks lobbied against it, Miliband said.

"What greater evidence could there be that this government has neither the inclination nor the capacity to bring the change that Britain needs?" Miliband told the Fabian summer conference.

But Miliband suffered embarrassment on Sunday when Alistair Darling, the former Labour chancellor, said there was no need for a full inquiry into the banking industry of the kind proposed by Miliband. "We know what went wrong and we don't need a costly inquiry to tell us," Darling told the Sun on Sunday.

Cable also said that he himself did not see the need for a full inquiry. "We already know that there is rampant greed and corruption in parts of the banking system," he said. "The question is taking action on it. Having a very long, expensive inquiry doesn't necessarily take the subject on."

Cable also said that he thought parliament could carry out an investigation itself. "Parliament and the Treasury select committee is a very effective, and very open and public forum for having people interrogated," he said. "My instincts are that parliament's probably the best place to do this."

This has also been the view of the Chancellor who has welcomed the decision by MPs to call the Barclays executives to give evidence this week.