By Andrew Bryson
Senior Liberal Democrats want the government to give away billions of pounds of its shares in Royal Bank of Scotland and Lloyds Banking Group to the general public.
The radical idea would see most of its stake in the banks shared between 46 million adults on the electoral roll.
A floor would be set so the shares could not be sold until they had passed the price paid by the government.
Individuals would only keep any gains made above that floor price.
The government spent £65.8bn buying shares in the banking giants.
It owns 83% of RBS and 41% of Lloyds.
The idea is set out by Stephen Williams, Liberal Democrat MP for Bristol West, in a pamphlet for the think tank Centre Forum.
He said: "There is a danger that when the banks return to the private sector, it is business as usual. There is a general feeling in this country that we need to get something positive in return for the bail-out.
"This plan would recoup the public's investment and allow the taxpayer to get the benefit from any increased value in the banks."
Under the proposal, shares would be deposited in individual trading accounts.
Mr Williams told the BBC how he saw the plan working: "Every citizen would have the same rights as shareholders at the moment, so they'd have the rights to get the company annual report. They could turn up at the AGM.
"What might happen, for instance, is there could be shareholder associations set up of citizens who own these shares, who will put pressure on the banks to change their behaviour. Banks and all other companies are meant to be owned by their shareholders and to respond to their shareholders' wishes."
At current prices, every adult would receive shares worth just under £1,000.
Each account would be set up with a default option to sell the shares over two or three years, although individuals could opt to hold the shares for longer.
The idea may have popular appeal - but it was not conceived by politicians.
The city firm Portman Capital devised the model for the Liberal Democrats as a way round some of the problems the government could face in a traditional share sale.
Privatisations in the 1980s saw shares offered at a big discount.
That tempted institutional investors to buy in, but led to criticism the government was "selling the family silver" off too cheaply.
In 2008 and 2009 the government injected approximately £45.5bn into RBS by buying shares, and £20.3bn into Halifax Bank of Scotland, which was taken over by Lloyds.
UK Financial Investments, which manages the public's stakes in the banks, is currently expected to sell them through conventional means.
That is likely to include placing the shares with pension funds and sovereign wealth funds, as well as offering them to retail investors.
UKFI is likely to have to stagger the sale of the shares over a number of years in order to get the best price so that the market has time to absorb the huge amount of shares on offer.
The shares are currently trading a few pence below the government's "break even price" of 51p for RBS shares, and 74p for Lloyds.
Toby Fenwick from Portman Capital says the shares suffer from an "overhang" - a situation where the market knows a lot of shares are likely to be sold and consequently depresses the share price.
"Under the current scenario there is one seller with a very big stake to unload and the market knows its break-even price," he said.
"A share distribution would create a new scenario with tens of millions of sellers each with a small stake and no incentive to sell below the 'floor'."
The idea is backed by Mr Williams and Lord Dick Newby, the Liberal Democrats' Treasury spokesman in the House of Lords.
It is not official Liberal Democrat policy, although the party's ministers are understood to be sympathetic to exploring whether the idea would work.
A source close to Danny Alexander, the Liberal Democrat Chief Secretary to the Treasury, said: "No decision has been taken about how or when this issue is going to be dealt with. But this is a welcome contribution to the debate."
Reproduced with acknowledgements to BBC News