Millions of taxpayers should be given the chance to profit from a no-risk stake in Royal Bank of Scotland or Lloyds, according to a think-tank.

Every voter would be given the opportunity to hold shares in the state-backed banks and take the profit on selling them while the original price of the stock would be returned to the Government, under the proposal by Policy Exchange. The think-tank said it would create a new generation of shareholders and allow the Government to dispose of its stakes in the banks before the 2015 general election and at a better price than with other options.

RBS and Lloyds were bailed out during the financial crisis and the Government now owns 81% and 39% of the companies. Chancellor George Osborne is reportedly due to outline his plans for the disposal of Lloyds at his Mansion House speech to the City later this month.

Under the Policy Exchange scheme, £34 billion of the Government's total £48 billion stakes in the two banks would go into the hands of individual taxpayers. The plan would see all British residents aged over 18 with a National Insurance number and registered to vote - representing up to 48 million people - allowed to apply for shares worth up to £1,650.

The idea comes in a report, Privatisation of the Banks: Creating a new generation of shareholders, authored by James Barty, former global head of equity strategy at Deutsche Bank. Examining all options available to the Government, it concludes that a distribution of shares in both banks to taxpayers - to be repaid on sale - combined with a sell-off to investors and institutions, is the best solution.

It says that shares would be distributed to taxpayers who would be able to apply for them at no initial cost. They would be paid for at the time of sale. In the event of shares never exceeding an initial "floor price", they would return to the Government after 10 years, giving taxpayers confidence since there would be no downside or upfront cost.

The shares would be held in a special nominee account. Taxpayers could buy them for themselves by paying the Government the floor price. Those not wanting to manage the shares on day-to-day basis could choose an automated option, for example selling all their shares once the price had risen by 20%.

The report found flaws in other options to re-privatise the banks. It said a staged sale to institutions could not take place before the next election and shares would have to be sold at a discount.

A mass share sell-off along the lines of BT or British Gas would allow the Government to sell a bigger stake by getting retail investors involved but they would need to be tempted by a "sizeable discount". In addition, the cut would have to be offered to all EU citizens. Also, only wealthier taxpayers would have the means to participate in the share purchase.

Meanwhile a share giveaway, costing £50 billion, was described as a non-starter, especially as those receiving the stock would look to cash in by selling quickly, putting pressure on the share price.