Pledging a "day of reckoning" for those behind the turmoil, the Tory leader said rooting out the culprits was essential to restore confidence in the financial services sector.
He also accused Gordon Brown of a "failure of moral leadership" for not urging the authorities to probe scandals in the City.
In a speech at Thomson Reuters in Canary Wharf, home of thousands of City workers, Mr Cameron said the rich and well-connected should not be protected from the law.
While claiming the Government was most to blame for the financial crisis, he said Labour's "economic policy mistakes" were compounded by "irresponsible" behaviour in the City.
He went on: "Doctors who behave irresponsibly get struck off. Bankers who behave irresponsibly should face professional consequences.
"And, for sure, if anyone is found to have behaved criminally they must be prosecuted.
"Of course, this requires clear evidence of wrongdoing. But that doesn't mean we should sit on our hands and say it's all a failure of regulation."
The Conservative leader said there was evidence of mortgage fraud, "possible" insider trading and other misconduct investigated but not prosecuted by the Financial Services Authority.
"To send out the right message about our country's values to help stop this crisis from happening again and to help restore the City of London's reputation I believe it is now vital that investigations are vigorously pursued to their appropriate conclusion," he went on.
"And the fact that the Prime Minister has not been urging our authorities to pursue financial wrongdoing, like in America, is in my view a failure of moral leadership."
Mr Cameron said there was a lack of will in Britain to see justice done "at the highest level", either from the Government or the FSA.
"The FSA and the Serious Fraud Office should be following up every lead, investigating every suspect transaction," he said.
"And the Government should be urging them on, because we need to make it 100% clear - those who break the law should face prosecution."
In the US, large financial institutions were being investigated by the FBI and the Securities and Exchange Commission, the Tory leader said.
"We all know there was poor decision-making and some reckless activity in the City of London," he added.
"But we do not know if there was wrongdoing and the nature of any wrongdoing, because we haven't examined the issue thoroughly in the way the Americans are doing."
He called for a bigger levy on the City to pay for the "best possible staff" for the FSA, which in turn had to force firms to hold more capital to offset high risks.
Mr Cameron added that the City would not recover from the financial crisis unless it regained confidence, and that meant holding those responsible to account.
"In the good times, some people working in the financial services industry paid themselves vast financial rewards - salaries and bonuses beyond the comprehension of most of us," he said.
"Now, when it's all gone wrong, they have been bailed out by the taxpayer.
"Nurses and cleaners and teachers and many millions of others, working in every part of our economy, they will foot this multibillion-pound bill.
"Well, on behalf of the taxpayer, on behalf of the nurse on £20,000 a year, on behalf of the cleaner on the minimum wage, on behalf of working families worrying this Christmas like never before about what next year will bring, I say it is fair and reasonable that those responsible are held to account for their behaviour and that we show clearly that, in this country, there is not one rule for the rich and a different rule for everybody else."
He said that more than a million people who work in the financial services industry had had their names blackened by the crisis.
"It's in their interests too that we make sure we root out any wrongdoing that may have happened, whoever is involved, however high or well-connected they may be," Mr Cameron added.
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