The former bank bosses apologised for their part in the crisis
The government is being urged to ensure that in future the chief executives of Britain's banks have a "recognised banking qualification".
The call has come in a Commons motion, tabled by the Labour MPs Gordon Prentice and Paul Flynn.
It follows the admission in a select committee hearing from former bosses of the RBS and HBOS that they did not have any banking qualifications.
Both banks were "bailed out" with £37bn of taxpayers money.
The four former bosses of the two biggest UK casualties of the banking crisis apologised "profoundly and unreservedly" for their banks' failure in a select committee hearing on Tuesday.
The former bank chiefs admitted they failed to predict the collapse of wholesale banking markets and said the bonus culture had contributed to the crisis and needed to be reviewed.
All four were quizzed by MPs on the Treasury Committee on their qualifications for running large retail banks.
Sir Tom McKillop, former chairman of the Royal Bank of Scotland who admitted its £50bn takeover of ABN Amro had been a "bad mistake", said he did not have any formal banking qualifications.
When the Conservative MP Peter Viggers asked Sir Tom, a former ICI research scientist and ex chief executive of pharmaceuticals giant AstraZeneca, if he had understood the full complexities of the financial instruments devised by the "clever young men" at RBS, he replied: "You said 'full complexities'. I would say no."
Former RBS chief executive Sir Fred Goodwin, who has spent almost his entire career in banking, told the committee: "I don't know whether you would call them banking qualifications but I have a degree in law and I qualified as a chartered accountant."
Andy Hornby, former chief executive of HBOS who entered the world of banking in 1999 after a career in retail, said he had an MBA from Harvard, "where I specialised in all the finance courses including financial services".
His former chairman at HBOS, Lord Stevenson, a former management consultant who became director of Halifax in 1999 prior to its merger with the Bank of Scotland, said he did not have any formal banking qualifications.
There are few qualifications suitable for someone running a large retail bank.
The Financial Services Authority has the power to block board-level appointments to British banks, and since last year has subjected all applicants to an interview.
But an FSA spokesman said it concentrated more on whether candidates had the right experience and were "fit and proper people" rather than any formal banking qualifications they might hold.
Lord Stevenson told the Treasury committee it was difficult to find non-executive directors with the right banking experience to join boards.
At a more junior level, there are many degree courses in finance studies and economics but most retail banking graduate training schemes will accept any discipline.