Labour leader Ed Miliband has said banks must not be isolated from the rest of UK society and must end a "culture of excessive bonuses".
In a speech he called for "one nation" banks, serving every region, business and family.
He said banking was at a crossroads after rows over bonuses and a decision to rescind Fred Goodwin's knighthood.
Tory MP Matthew Hancock said Mr Miliband "refused to accept his part in the economic mess Labour created".
Mr Miliband's speech, in London's financial district Canary Wharf, said calls for action were driven not by "the politics of envy" but the need for "values of fairness".
His comments come at the end of a week in which RBS boss Stephen Hester waived a £963,000 share-only bonus amid political anger and his predecessor at RBS, Mr Goodwin, was stripped of his knighthood.
'Culture of responsibility'
The Labour leader argued that the debate must not be confined to individual cases but focus on the wider issue of the role of banking in economy and society.
"This is about more than one man, one bonus, or one knighthood," he said.
"It is not about the politics of envy. It is about a culture of responsibility. We need what you might call 'one nation banking'. We need banks that serve the real economy. We need banking serving every region, every sector, every business, every family in this country."
Banks have played a valuable role in the past in promoting enterprise, helping new industries develop and old ones restructure, Mr Miliband said.
However, he said that bank lending fell £10.8bn last year and that if the industry "continues on its current path" it risks becoming "further isolated" from society and provoking greater "public anger".
"This is a call on banking to recognise it has reached a crossroads. This is a call on banking to recognise that it should take the path of change."
He also said banks had accepted "they bear the burden of responsibility for helping to cause the crisis".
"The consequences of their reckless irresponsibility in that era are felt every time a library closes, every time a school can't afford a new book and every time a policeman or policewoman is taken off the beat."
The Lord Mayor of the City of London, David Wootton, told BBC Radio 4's World At One programme he agreed with some of the points raised by Mr Miliband, but called for a "calm debate".
"Language of an emotional nature, I think, is useful in some respects but we do need a calm, rational debate. The banking sector has indeed accepted a degree of responsibility but others were responsible too," he said.
The term "one nation Conservatism" has traditionally been used by Tories who regard social justice and equality as as much of a priority as economic freedom and opportunity.
Mr Miliband said Labour intended to press ahead with a Commons debate and vote on City bonuses tabled in the wake of the row over Mr Hester's bonus.
But Conservative MP Matthew Hancock, who was Chancellor George Osborne's chief of staff when the party was in opposition, said: "This is just more empty rhetoric from a weak Labour leader.
"Ed Miliband calls for responsibility from bankers but has refused to accept his part in the economic mess Labour created."
He added: "Until Ed Miliband admits Labour's past mistakes, the public won't take his party seriously."
The government has said that its package of reforms will ensure banks have to publish more details about what their top earners are being paid, as well as giving shareholders binding votes on pay.
The Institute of Directors and other City groups have warned that the recent outcry over bonus awards and Fred Goodwin being stripped of his honour risk creating "anti-business hysteria".