David Cameron has announced a parliamentary inquiry will be held to "get to the truth" about the rate-fixing scandal that has rocked Barclays bank.
Speaking in the House of Commons on Monday afternoon, the prime minister said the inquiry would be headed by the chairman of the Commons Treasury committee, Andrew Tyrie, and with the power to take evidence under oath.
"It will be able to start immediately and it will be accountable to this House and it will get to the truth quickly."
"The British people want to see two things: That bankers who act improperly are punished, and that we learn the broader lessons of what happened in this particular scandal."
His comments came as the Serious Fraud Office said it was considering whether to bring criminal prosecutions in relation to the rate-fixing scandal, which has so far claimed the job of Barclays chairman Marcus Agius.
But Miliband told the Commons that a parliamentary inquiry into the activities of the banks was not good enough and called for a "full independent" inquiry into both bankers and politicians.
"Politicians investigating bankers will not command the consent of the British people," he said.
"I don't believe the proposed way forward is a way we can build the consensus of what is required."
Both Labour leader Ed Miliband and shadow chancellor Ed Balls were special advisers and ministers in the last government, with Balls serving as City minister between 2006 and 2007.
The Labour leader suggested that Cameron did not want to launch a independent inquiry as he had been burned by the Leveson inquiry into press ethics.
"The Leveson inquiry has been unconformable for politicians on all sides ...but that's the way it should be," he said.
But the prime minister rejected the suggestion he was scared of such a inquiry, telling MPs that he wanted a parliamentary inquiry as it could be conducted quickly.
"No one would want to see him in the dock of a court room more than me," he said of Ed Balls, who he often clashes with in the Commons.
Bob Diamond has made clear he is staying on as Barclays CEO, writing in an email to staff it is his "responsibility to make sure" another scandal cannot happen again.
His statement comes hours after the bank's Chairman, Marcus Agius, stood down in the wake of the Libor scandal, where Barclays was fined £290m for manipulating the rate at which banks lend to each other.
Diamond wrote to staff at Barclays: "It is my responsibility to make sure that it cannot happen again. I love Barclays and am proud of all of you.
On Monday morning Miliband repeated his call for Diamond to step down as CEO of the bank in the wake of the scandal.
Deputy prime minister Nick Clegg has also heaped pressure on Diamond, saying the "buck stops at the top."
"I'm like everybody else in this in that now that the chairman of Barclays has fallen on his sword and has taken responsibility for what has happened, everybody is asking when are the other senior people at the top of Barclays going to take responsibility for the things that happened on their watch," he said.
"I don't think it is for politicians to individually hire and fire bankers, but I do think the buck stops at the top."