Negotiations began on Thursday between the government and Labour over setting up a parliamentary inquiry into the banking scandal rocking the City of London, with the promise that it could begin work in two weeks.

After a bad-tempered Commons debate, MPs voted by a majority of more than 100 to set up a joint committee of MPs and peers to conduct the inquiry after earlier rejecting a Labour proposal for a judge-led public inquiry similar to the ongoing Leveson investigation into press standards.

However, there was confusion over what the committee would be examining and whether the government's hope that a report could be produced before Christmas was possible.

Following the vote, the shadow chancellor, Ed Balls, said Labour would respect the decision and cooperate with the inquiry. Balls said, though, that he would keep arguing for a wider inquiry. "The prime minister and the chancellor have made a very grave error of judgment," he said. "And any time any future scandals emerge, people will ask, why are we not having the full independent inquiry that this country needs?"

In the Commons debate, George Osborne traded insults with Balls in a row triggered by an interview published in the Spectator in which the chancellor said people working with Gordon Brown under the last Labour government were "clearly involved" in the scandal of manipulation of the interbank lending rate, Libor. Osborne claimed the "Brown circle" included Balls and that he had "questions to answer".

Balls demanded Osborne provide evidence of his accusation or retract it and apologise. Balls said the allegation was "utterly false". He told Osborne: "The cheap and partisan and desperate way in which you and your aides have conducted yourselves in recent days does you no good. It demeans the office you hold and, most important, it makes it harder to achieve the lasting consensus we need."

Osborne pointed to testimony to the Treasury select committee on Wednesday by former Barclays chief executive Bob Diamond that ministers in the previous government had been keen for the Libor rate to be lower. Diamond made the remarks when he was asked to identity the senior Whitehall figures in a memo he wrote after a conversation with the Bank of England deputy governor Paul Tucker in 2008.

"The idea that I'm going to take lessons in integrity from the man who smeared his way through 13 years of Labour government … is another thing," said Osborne, who also cited the admission by Balls's former colleague at the Treasury, Lady Vadera, that she had seen a report by the Swiss bank UBS on reducing Libor rates.

Treasury aides tried to dampen the row by indicating that Osborne had not named Balls when he spoke of ministers who were "clearly involved". James Forsyth, the Spectator's political editor who interviewed Osborne, tweeted: "NB Osborne didn't say Ed Balls was the one who was 'clearly involved'. But that 'he has questions to answer as well'."

A treasury source reinforced this by saying: "We stand by the original claim. What George said was that as city minster for much of the period Ed Balls has questions to answer – that remains all too true."

But treasury attempts to claim Osborne had merely said that Balls had questions to answer – and had not linked the chancellor to his more explosive allegation that he was "clearly involved" in attempting to influence the Libor rate – were undermined by a Tory party press release. Issued within hours of Bob Diamond's evidence to the treasury select committee on Wednesday, this was entitled: "Bob Diamond evidence points finger at Gordon Brown, Ed Balls and Shriti Vadera as the 'senior figures' trying to fiddle Libor."

Balls, who was children's secretary in 2008, said he had never had such a discussion about Libor. Vadera said it was sensible for officials and ministers to be interested in the Libor rate during such a major financial crisis.

Labour called the debate after a week-long dispute over who should lead an inquiry and what it should cover following revelations last week that traders at Barclays had manipulated the Libor rate between 2005 and 2009 to make it look lower and therefore reduce concerns about the bank's stability.

Opening Labour's debate, Balls rejected the government's reasons for opposing a Leveson-style public inquiry. He said the problems with the banking industry were "much, much wider" than the Libor problems and so merited a wider inquiry; Labour's plan would enable MPs to have a report on the Libor-fixing scandal by Christmas, before the expected banking bill in January; and a public inquiry would have greater powers to force witnesses to give evidence under oath and request documents. "Only a judge-led inquiry can persuade the public the inquiry is truly independent and objective," Balls said.

Osborne said wider banking issues had been considered by the Vickers commission on banking, which reported in 2011 and is to be the basis of a banking bill early next year.

The chancellor insisted the proposed joint committee of MPs and Lords could be given tough powers, using standing orders or legislation if necessary.

There was uncertainty over the speed of the parliamentary inquiry after the attorney general, Dominic Grieve, made a rare intervention in the debate to tell MPs that Labour's suggestion for a two-part inquiry, firstly into Libor and later into the wider banking culture, could clash with ongoing criminal investigations into the Libor rigging, throwing the government's own timetable into doubt.Grieve had been "very helpful", said Balls.

Earlier in the day, Labour leader Ed Miliband visited a small business in Putney, west London, which has had to lay off staff after being advised to take out a loan on a 10-year swap. Henderson Signs, which makes signs for estate agents and auctioneers, has lost £400,000. Under the highly complex arrangements with NatWest and RBS, the company found the interest charged on its loan increasing dramatically wheneven though the Bank of England base rate fell during the credit crisis.

Miliband said: "I will be demanding that the FSA widen its scope to make sure the people like the Hendersons are included. We can't have a situation where people like them, who have so clearly been fleeced in the most reprehensible way, are excluded."