A "Robin Hood" transaction tax on banks would raise as much as $400bn (£250bn) a year, campaigners have said.
Supporters say money raised could help protect public services and jobs, fight poverty and tackle climate change.
The campaign is backed by almost 50 groups, including the TUC and Oxfam, and celebrities like actor Bill Nighy.
Mr Nighy told BBC Radio 5 Live: "This is a tax on speculative banking, the kind of gambling that went on that got us into trouble."
"The banks have been bailed out to the tune of 9 trillion dollars. It's symmetry that the banks should therefore not only make good the damage caused by the economic crisis but should also perpetually become a useful thing in society."
In recent months governments and bankers have mooted similar plans - but their focus is insuring against future banking crashes.
Last month, the World Economic Forum (WEF) discussed a levy on financial institutions that would be used to help bail out banks in any future crisis. The call was backed by politicians and the International Monetary Fund (IMF) at WEF's gathering in Davos.
Meanwhile, the European Union has been calling on the IMF to back the plans for a so-called "Tobin Tax" on international transactions.
The tax, named after the Nobel Prize-winning economist James Tobin, was originally designed to discourage volatile currency trading and also had the potential to help developing nations, but many supporters now say it is one way to ensure that banks do not take excessive risks that could trigger another financial crisis.
'Radical new option'
Let's turn the crisis for the banks into an opportunity for Britain and the world
Under the Robin Hood Tax plan, the tax would not be levied on banks' transactions with their High Street customers.
Instead it would only apply to transactions between financial institutions, with different rates applied to different types of transaction - with an average tariff of five pence for every £1,000 traded.
The campaign is calling for countries that levy the tax to keep half the proceeds domestically and for the rest to be split 50-50 between poverty reduction and tackling climate change.
According to the group the tax could raise tens of billions of pounds for the UK, which it says could be used to help cut the public deficit.
In a letter to the leaders of the UK's political parties, the campaign says: "We would ask you seriously to consider the Robin Hood Tax as that radical new option - a small tax on bankers that would make a huge difference to the UK, to the poorest countries and to our planet.
"Let's turn the crisis for the banks into an opportunity for Britain and the world."
However, any plans to implement an international tax would need international backing - and any plans for similar measures have received a less than lukewarm welcome from the US and IMF.
At a meeting of G20 finance ministers last year, IMF head Dominique Strauss-Kahn described a tax on financial transactions as "a very old idea that is not really possible today".
The UK's British Bankers' Association also questioned the feasibility of the scheme. Spokesman Brian Mairs said it was fatally flawed, "because it requires all of the world's tax jurisdictions to agree to it, all at once. It's inconceivable and impractical at this stage".
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