In a speech in London's Canary Wharf financial district, the Labour leader urged a return to "one nation banking" which would serve the wider economy and society.
His appeal came at the end of what he called a "turbulent" week for the banking industry after disgraced former Royal Bank of Scotland chief Fred Goodwin was stripped of his knighthood.
Mr Goodwin's successor at the majority state-owned bank waived his almost £1 million bonus amid intense pressure from politicians and the public.
Mr Miliband told the bankers in his audience at the Thomson Reuters Building that they needed to reflect "the values of Britain".
"We cannot have a banking sector so divorced from the rest of the economy and the rest of society," he said.
"We succeed or fail together. 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.
"And we need banks run in a way that people believe are consistent with their values - the values of Britain."
He added: "Responsibility means ending the culture of excessive bonuses."
The Labour leader warned of a return to "two nations", the description of 19th century Britain used by Victorian Conservative prime minister Benjamin Disraeli.
The banking and financial sector was on a path of "gradual separation from the rest of society", he said.
"We are once again at risk of becoming a country separated economically, geographically and socially," he went on.
"We are once again at risk of becoming two nations in this country.
"That is not the kind of society in which I want to raise my children.
"And it is not the kind of society in which the vast majority of people in this country - including bankers - want to raise theirs."
Mr Miliband said banks, effectively underwritten by the taxpayer, could not be "immune" from public debate.
"This is a call for banking to recognise that continuing on its current path will lead to further isolation from society, greater public anger, more years in which each payday is a newspaper headline," he said.
"This is a call on banking to recognise that it should take the path of change, to recognise that it is not isolated from the economy or society."
In a question and answer session following his speech, Mr Miliband said the public sector must set "the best example" when it comes to high pay,
as he pressed ministers to reveal who signed off the tax arrangements of Student Loans Company boss Ed Lester.
Earlier in the week, it was revealed Mr Lester was paid through a separate company, which enabled him to avoid paying thousands of pounds in tax. Mr Miliband also criticised six-figure bonuses at Network Rail.
He said: "I have been very concerned about what I have seen on the bonuses at Network Rail because if politicians are going to be concerned about what are seen as excessive bonuses in the banking sector, I think we should be equally concerned with organisations like Network Rail."
He added: "On the question of the Student Loans Company and the way the payments were made, there are many unanswered questions.
"I think the most important question is what did ministers know and when did they know it? My impression from watching parts of the exchanges yesterday in the Commons with Danny Alexander suggesting he hadn't known... but as I understand it there are documents coming to light which suggest that he was informed about what was happening.
"Similarly with Higher Education Minister David Willetts, did he know what was going on? If they did know, did they think it was a good idea or a bad idea and did they sanction it?
"I think there are really unanswered questions here about what was going on at the Student Loans Company. And there continues to be a question of whether income tax and National Insurance is going to be paid.
"All us have to understand that times are different and it is particularly important that the public sector sets the best example it can. These aren't just issues for the banking sector, these are issues which are broader as well."
PA
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