The Government defeated the move with MPs voting by 320 to 239 against the proposal - a majority of 81.
The House of Commons backed a Government plan to set up a joint committee of MPs and peers to investigate the banking industry by 320 votes to 226, majority 104.
Shadow chancellor Ed Balls said Labour would take part in the parliamentary probe, which will be led by Treasury Select Committee chairman Andrew Tyrie, but would keep up calls for a wider-scale investigation, insisting that the case for an independent inquiry was stronger than ever.
Both votes followed a highly-charged debate in the Commons on how to investigate the cultural and professional standards of Britain's banks after revelations about the practices of some traders at Barclays (LSE: BARC.L - news) sparked an outcry.
Labour insists an independent "forensic" judicial inquiry, along similar lines to the Leveson inquiry into the media, is the only way to restore public faith in the disgraced industry.
The coalition argues that a parliamentary investigation is the best way to get speedy recommendations that can be included in a banking reform Bill early next year.
However, the Government's most senior lawyer, Attorney General Dominic Grieve, warned both proposals could undermine a potential criminal investigation.
He told the Commons: "If there are criminal investigations or enquiries then it will be difficult."
Ahead of the voting, Chancellor George Osborne and Mr Balls were locked in angry exchanges over allegations the shadow chancellor was involved in the scandal.
Mr Balls was furious over an article in The Spectator magazine in which Mr Osborne said he had "questions to answer" over alleged pressure from the then Labour government on Barclays to fix a key lending rate called the Libor.
Former Barclays chief Bob Diamond noted in a memo in October 2008 that the deputy governor of the Bank of England Paul Tucker had passed on concerns from "senior figures in Whitehall" that the bank's Libor was too high.
In his evidence to the Treasury Select Committee on Wednesday, Mr Diamond refused to speculate about their identity but the Tories have pointed the finger at Mr Balls and former Treasury minister Baroness Vadera.
Both have denied any involvement and in the Commons, Mr Balls demanded that Mr Osborne withdraw the "false, personal accusations".
The debate descended into a highly partisan row as the two men exchanged jibes and Mr Osborne went on to accuse Mr Balls of "smearing" his way through 13 years in office.
As they traded blows, it was confirmed that Mr Tucker will appear before the Treasury Select Committee himself on Monday where he will be asked to shed light on the affair.
As the spotlight on Barclays continues, the bank's credit rating outlook has been downgraded to "negative" from "stable" by two ratings agencies due to fears sparked by the shock resignation of Mr Diamond.
Labour leader Ed Miliband has claimed David Cameron will be ignoring the "national interest" if he refuses to hold a full-scale inquiry.
At PMQs on Wednesday, he suggested a two-stage probe with the first examining issues surrounding the London inter-bank offered rate (Libor) and reporting by Christmas and a second looking at the wider sector.
According to Labour's motion being put to the Commons, the whole inquiry would be wrapped up by summer 2013 and the cost would be met by the banking industry.
It has been backed by the DUP, SNP, SDLP, Plaid Cymru, Green Party and Independent MP Sylvia Hermon.
However, MPs on all sides are expected to be whipped to back the party line in the votes which means it is likely to be defeated by the Tory-Lib Dem united front.
Mr Balls made clear during the debate that Labour will continue to argue for a full public inquiry even if it loses,
Tory MP Andrew Tyrie, the chairman of the Commons Treasury Committee who has been chosen to chair a parliamentary inquiry, said he will not go ahead unless it has cross-party support.
The Government is expected to find a replacement if he stands aside, although this will risk undermining its legitimacy before it has even begun.
Mr Cameron insisted on Wednesday that there was no difference between him and the Opposition on the seriousness of the rate-rigging scandal.
"It is outrageous, frankly, that homeowners may have paid higher mortgage rates and small businesses may have paid high interest rates because of spivvy and probably illegal activity in the City," he said.
"People want to know that crime in our banks, crime in our financial services will be pursued like crimes on our streets."
However, he said he believed that a parliamentary inquiry was the quickest way to get to the bottom of the problems.
"The most important thing about an inquiry is that it is swift and decisive, set up as fast as possible, gets going as fast as possible, reports as fast as possible - transparent and open at every stage," he said.
"That's why I favour a public parliamentary inquiry rather than a judge-led inquiry."
Mr Miliband countered: "If he fails to order a judicial inquiry, people will come to one conclusion: he simply can't act in the national interest."