His solution, he said, was for "a recapitalisation to strengthen the banking system", rather than a British version of America's Hank Paulson plan.
"It's something parties should talk about, and I think it's something where consensus would be better than opposition."
He said that changes are needed to the way that bonuses are awarded in the City of London and he did not rule out a future need to guarantee all deposits in British banks.
"You shouldn't rule that out, and that may become appropriate, but I think part of the problem with that is that you are dealing with the symptoms rather than the underlying cause", he said.
We've got a government that is divided and dysfunctional, and I think this [Mandelson's return] will make it more divided and more dysfunctional
Blair close to Blair
He also spoke about the removal from office of the Commissioner of the Metropolitan Police, Sir Ian Blair. He said he agreed with the actions of the Mayor of London, Boris Johnson, and criticised Sir Ian's closeness to New Labour.
"I think he showed a number of misjudgements in that direction. I don't think that's the only reason, but that didn't help."
On the return of Peter Mandelson to the Cabinet, Mr Cameron was critical.
"I think it's a pretty desperate move, really. We've got a government that is divided and dysfunctional, and I think this will make it more divided and more dysfunctional.
"To me, this is about trying to shore up the Labour Party, it's not about trying to serve the country. They're looking at their own problems to try and save Brown, whereas actually what is needed is a government that is really unified, like my party is, that can actually serve the country."
The general election coordinator is going to be Douglas Alexander
Labour's Deputy leader, Harriet Harman, also spoke to the programme about the return of Peter Mandelson.
She announced that he would not be running Labour's General Election campaign.
"The general election coordinator is going to be Douglas Alexander.
"Ed Miliband is going to continue to draw together work on the manifesto and obviously, I'll continue to chair the Party", she said. However, She praised Mr Mandelson's return to the Cabinet.
"I think that what the prime minister has done is he wants to strengthen our economic team... it's a time of great national challenge on the economy and Peter Mandelson is admired and respected for the work he's done in Europe and internationally," she said.
Boris Johnson gave his first big interview to the Politics Show since last week's resignation of Sir Ian Blair.
Mr Johnson dismissed talk of political interference in the Police as "codswallop, tripe, balderdash".
"Some of the things I've read," he said, "have been on the wilder shores of fantasy. This was simply a decision reached as a result of a discussion about how to improve the operational effectiveness of the Metropolitan Police and give someone else the chance to offer new leadership in London."
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