Marcus Agius has quit as chairman of Barclays, saying he was "truly sorry" for the interest rate-rigging scandal that has dealt a "devastating blow" to the bank's reputation.

Chancellor George Osborne is expected to make a statement to MPs on Monday, with Agius's resignation yet to puncture the political pressure on the bank.

The Labour leader, Ed Miliband, is calling on the bank's chief executive, Bob Diamond, to quit and has stepped up his efforts to force the government to set up a Leveson-style inquiry into banks by bringing forward an amendment in parliament.

"I think there needs to be more a more general change of leadership including the chief executive, Bob Diamond," Miliband told ITV Daybreak.

The bank put board director Sir Michael Rake, the former top accountant and serial company director, in the new key role of deputy chairman to oversee an audit of the bank's business practices, the findings of which will be published.

A "zero-tolerance policy" will be adopted against staff who damage the bank's reputation and a new code of conduct drawn up, which all staff will need to adhere to.

After a wave of political fury was unleashed by a record £290m fine for the bank's attempt to manipulate key interest rates, Agius described himself as the "ultimate guardian of the bank's reputation".

He said "last week's events – evidencing as they do unacceptable standards of behaviour within the bank – have dealt a devastating blow to Barclays' reputation. As chairman, I am the ultimate guardian of the bank's reputation. Accordingly, the buck stops with me and I must acknowledge responsibility by standing aside," Agius said.

Rake is expected to be considered as a candidate to replace Agius in a search process that will be led by the former Cadbury boss Sir John Sunderland. The search – from within the existing board members and from outside – will begin immediately and Agius will stay until his successor is found. The process may be drawn out as the Financial Services Authority, the City regulator, needs to authorise the candidate.

The audit of business practices will be conducted by an external company, which will undertake a "root and branch review" of all the business practices since the credit crisis.

"This exercise will be part of a broader programme of activity intended to restore Barclays' reputation and we will establish a zero-tolerance policy for any actions that harm the reputation of the bank," said Agius.

"I am truly sorry that our customers, clients, employees and shareholders have been let down. Barclays is full of hard working, talented individuals whose integrity is not in question."

Agius, who earns £751,000 a year, is still expected to appear before MPs on the Treasury select committee on Thursday – the day after Diamond, whose role in the interest rate-fixing scandal will take centre stage after it emerged he had personally spoken to the Bank of England about the rates being set.

The bank's annual report shows that the chairman can receive "potential compensation for loss of office" of 12 months' fees. It was not immediately clear on Monday morning if any compensation would be paid.

Diamond showed no signs of tendering his own resignation on Monday. Instead he expressed his gratitude to Agius. "Marcus has shown a remarkable passion for Barclays and its people," Diamond said.

But the pressure on Diamond remained. Liberal Democrat peer Lord Oakeshott said: "Bob's still got to go. Barclays simply isn't safe in his hands. The board is so hopeless they've just shot the head of the firing squad and missed the prisoner."

Gary Greenwood, banks analyst at stockbroker Shore Capital, said Agius's departure would "do little to appease the many who see Bob Diamond as having primary responsibility".

The bank was fined for attempting to fix interest rates, known as the London interbank offered rate (Libor) and the European equivalent, Euribor. These are two benchmarks that are the basis for pricing an array of financial products, potentially affecting the price at which households and businesses borrow money.

The Financial Services Authority fined the bank £59.9m, while in the US the department of justice and the Commodities Futures Trading Commission also imposed fines, some £230m combined.

The offences took place in two ways. First, from 2005, Barclays traders tried to alter rates to help themselves and rival traders. Second, in 2008 – when Barclays raised concerns about Libor – the bank is said to have kept rates lower because higher levels might have been misinterpreted as suggesting the bank was facing financial difficulties.

At one point, the documents released by the FSA showed that so-called submitters of the rates used to calculate Libor believed they were operating under the instruction of the Bank of England.

Paul Tucker, the deputy governor of the Bank of England, spoke to Diamond at the time although the Bank of England made clear on Sunday it had not known about the problems with Libor.

Fourteen Barclays traders in New York, London and Tokyo are implicated by the regulators but other banks are still the subject of investigations. RBS, for instance, has sacked four traders and up to 20 banks and financial firms are thought to be co-operating with international regulators.