A string of mis-selling scandals, rate-fixing and rogue traders has called into question the reputation of Britain's financial services. London lost the top spot in Long Finance's Global Financial Centres Index for the first time this year.
Read MoreShould bankers swear an oath to God?
The ResPublica report's authors, which were led by David Llewellyn, chairman of the Board of the Banking Stakeholder Group at the European Banking Authority, argued that an oath would install higher levels of personal responsibility among bankers.
"Consumer trust and confidence is at an all-time low. We believe that, if bankers were required to swear an oath akin to the Hippocratic Oath that doctors affirm, this would signal a serious commitment from bankers towards the pursuit of greater professionalism," they wrote in the report.
The proposed oath includes pledges to "do my utmost to behave in a manner that prioritizes the needs of customers" and to "confront profligacy and impropriety wherever I encounter it".
It's not the first time that a "bankers' oath" has been proposed. Starting next year, Dutch bank employees must swear an oath - optionally to God - promising they will perform their duties with integrity and that they will "endeavor to maintain confidence in the financial sector."
'Simply won't work'
But there are no such plans in Britain – and not everyone is convinced that, even if such an oath were introduced, it would make any difference.
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"It simply wouldn't work," former banker Joe Rundle, who now works as head of trading at ETX Capital, told CNBC. "It's trying to solve a problem that's been brought around by a lack of regulation and a lack of understanding. An oath isn't going to fix that."
But Rundle argued that the majority of banking scandals aren't caused by employees acting maliciously.
"These problems have been caused by the system – not the people in it," he added. "Bankers' risky behavior is carried out within the rules."
Read MoreFX rate fixing scandal could be worse than Libor
Following the financial crisis of 2008, an independent body for banking standards was created, in an effort to promote high standards of behavior and competence across the country's banking industry. It is headed up by Richard Lambert, who launched ResPublica's report on Tuesday, although he has not endorsed its recommendation of a bankers' oath.
The British Bankers' Association, which represents the U.K.'s banking sector, said restoring trust and confidence was the industry's "number one priority".
"It may be that the new standards review body decides that some within the industry should be subject to an oath or a code of ethics. It very well could be part of the answer," Paul Chisnall, the BBA's executive director for financial policy and operations, said in a statement.
—By CNBC's Katrina Bishop