Risk-free "safe haven" accounts guaranteed by the government should be set up as part of a "profound reform of the banking system", a report says.
The Future of Banking Commission wants improvements in saver protection and restructuring of banks.
The commission was set up by consumer group Which? and is chaired by Tory MP David Davis.
He told the BBC that big banks must be broken up in order to prevent another financial crisis.
"If we don't do something, next time [a crisis] happens it will break the country - it will go bankrupt," he told the Andrew Marr Show.
He said breaking up the banks would be "tough to do, but it's got to be done".
Earlier, Mr Davis said fatal flaws in the banking structure had almost crippled the world economy.
He said the commission's proposals should prevent matters coming to such a head again.
The commission, which was set up last December, gathered evidence from regulators, consumer groups and business leaders including Bank of England governor Mervyn King, the Financial Services Authority chairman Lord Turner and the current Business Secretary Vince Cable.
Its recommendations will be delivered to 11 Downing Street, with the hope that they will shape government's policy on financial reform.
Executives from the UK's largest banking groups contributed to the commission and it also took evidence from consumers.
The commission says its recommendations aim to put ordinary people at the heart of a reformed banking system.
They include reforms to the structure of banks so if they fail, depositors are protected, and the introduction of new competition and regulatory regimes that make bank boards responsible for both meeting customers' needs and for their own solvency.
Other ideas include an "ethical culture" which would see banks stop paying commissions to front-line staff.
"We have made recommendations to minimise the conflicts of interest inherent in banking, and to limit the liability of the taxpayer and thereby reduce the risk to the economy," Mr Davis said.
"We also propose a structure and regulatory regime designed to entrench a stable and competitive banking sector for the long term."
Other recommendations by the commission include so-called "living wills" detailing how the collapse of a bank would be managed and how customers would be treated, as well as giving banks' boards responsibility for the management and stability of their banks.
It says regulation should be used instead to increase competition among banks.
Improvements to depositor protection are also on the list, including a new class of "safe haven" accounts, which would only be invested in safe assets.
In return for guaranteed protection, investors would receive low returns. Under the current Financial Services Compensation Scheme, only the first £50,000 is protected.
The commission wants this limit to apply to each brand rather than to each licensed institution, which would give savers greater protection.
Jenny Driscoll, from Which?, said it was time for banks to change.
"I think if we've ever got the opportunity to sort out the banking system, it's now. And what Which? is doing is taking it forward, so that customers really do see the benefits following this," she said.
"We want to hear from them, we want to hear banking nightmare stories, and we're really going to put the pressure on the banks to change, and also on the government to sort things out once and for all."
The Department for Work and Pensions said "simplification" was an "important part of the government's agenda".
"The government is committed to reinvigorating private pensions and welcomes contributions to the debate, including on the issue of encouraging savings," it said.
The British Bankers' Association said it agreed with many of the report's objectives, but added that its members were already making changes to tackle underlying problems.
In a statement, it added that the industry had made many significant changes to the way it operated and could not "by any means be described as a return to 'business as usual'", as the report implied.
The commission was set up after a proposal by John McFall MP who, as chairman of the Treasury Select Committee, wanted to give the public a chance to air its views about the future of banking.
However, the independent think-tank NEF, the New Economics Foundation, said the recommendations were not far-reaching enough.
Tony Greenham, head of the Business and Finance programme at the think-tank, said: "These recommendations are a promising start in building a banking system fit for the needs of the economy and society.
"We must hope that Vince Cable heeds his own advice now he is in government and not that of the vested interests in the banking industry seeking to prevent the break-up of their 'too-big-to-fail' mega-banks."