Calls are growing for a "Leveson-style inquiry" into banking.
It follows Barclays being fined for trying to manipulate a key bank interest rate and the revelation that banks mis-sold specialist insurance.
Mark Garnier, a Conservative member of the Treasury Select Committee, said a process in which banks were "pulled over the coals" would address public fears.
But The Treasury said "action not words" is what is needed.
Sir Mervyn King, Governor of the Bank of England, said Britain's banks need a "real change in culture" but ruled out a wider inquiry.
Labour says a commission or inquiry into the culture and practices of the banking sector should be considered.
The TUC said is was "time for a fresh start" in banking and also backed an inquiry, as did the independent think-tank the New Economics Foundation.
On Thursday the Financial Services Authority's (FSA) fined Barclays £290m for trying to manipulate the inter-bank lending interest rate and the FSA has revealed some of Britain's biggest banks have mis-sold specialist insurance tied to thousands of small businesses.
Some MPs have called for Barclays chief executive Bob Diamond to resign and David Cameron has said the bank's management faces "serious questions".
Mr Garnier said the levelling of the fine on Barclays was a "game changing moment" which showed a "Leveson-style" inquiry was now needed to restore the public's trust in banks.
Lord Justice Leveson is carrying out an inquiry, which has already lasted more than 12 months, into the culture, practices and ethics of the media following the phone hacking scandal.
During the course of the inquiry new evidence has come to light and witnesses, which have included journalists, top politicians and victims of phone hacking, have been subject to lengthy and detailed questioning by a barrister.
Mr Garnier said: "The issue we had prior to yesterday (Thursday) was banks had been humongously irresponsible but had been acting within the rules and it was the rules that were the problem.
"What we see now is fundamental dishonesty and systemic and institutionalised behaviour.
"It's getting to the stage where there is now an interesting and compelling argument for having a more detailed look at it. A Leveson-style inquiry could dig deeper."
Labour's shadow business secretary Chuka Umunna echoed Mr Garnier's concerns: "Its not just isolated cases anymore.
"We now have a catalogue of scandal and wrongdoing. You can't dismiss this as a one-off and its insufficient to say its rogue traders. If ever there was a time to have this, its now."
He said a commission or inquiry into the culture and practices of the banking sector should be considered.
But Treasury Minister Mark Hoban told BBC News: "I think there have been a lot of inquiries. The Treasury Select Committee have done their own inquiry. We had the Independent Commission on Banking that we set up.
"I think what households, taxpayers and businesses want to see is action not words and we're taking the tough action that's needed to get the regulation right and help change the culture of banking in this country."