The Treasury and the Home Office confirmed yesterday that they had been in discussions with several building societies seeking to launch such accounts.
One proposal put forward by the Norwich & Peterborough, one of the most innovative building societies, has already been turned down by the Treasury.
Under the proposed schemes savers would forgo some or all of the interest on their balances in return for the chance to win big cash prizes. It is not clear whether such accounts would be legal in Britain under the 1976 Lotteries and Amusements Act.
One possible system would be to transfer account-holders' accrued interest into a prize draw which would offer large prizes every week, month or year. The more money a saver has in the account, the greater his or her chance of winning.
Such accounts would be similar to National Savings Premium Bonds. A National Savings spokesman confirmed it had made "one or two comments'' to the Treasury about the proposed schemes. National Savings took a net £1.4bn from sales of Premium Bonds last year.
Another option would be to offer both a small amount of interest and more modest lottery prizes. Such an option would be less likely to be outlawed by Britain's strict gaming rules.
Martin Armstrong, chief executive of the Norwich & Peterborough, said: "We did suggest to the Treasury that they might look at the possibility of allowing financial institutions to offer investment opportunities with a lottery element, but under the Lotteries Act they say it is illegal. We've suggested that they might legalise it."
The idea was condemned yesterday by the Bishop of Peterborough, the Rt Rev Bill Westwood, who said he would close his account if his building society introduced a lottery account. "Of course, can you blame them for following a national trend started by the Government? Inevitably they will want to get on this lucrative bandwagon. But what is this lottery mania doing to the soul of the country? A nation can only survive, let alone flourish, through hard work and endeavour, yet we are being whipped up into a culture of idleness and fortune."
A spokesman for the General Synod of the Church of England was equally opposed. "A building society is there to help you build up your savings, not encourage you to fritter them away."
But Mr Armstrong defended the idea, which comes from Japan, where lottery- based savings accounts are taking the nation by storm. Last autumn a small credit association, Johnan Shinkin, set up a deposit account with a lottery scheme attached. Within three days of opening, it had attracted more than Y14bn (£105m) in deposits.
Customers of the "Super Dream Account" win Y50,000 (£370) if their account number is picked. They still get interest on their savings, but not at a competitive rate. Over the next 12 months Johnan Shinkin expects to hand over Y4m in prizes.
Brian Waterhouse, a banking analyst at James Capel in Tokyo, said: "Now even the major Japanese banks, who were at first disdainful about going down such a tacky path, have followed suit." Mitsubishi Bank is now offering free trips to Disneyland.
Similar schemes are also emerging in Spain, where small to medium-size banks such as Banco Bilbao Vizcaya are offering prizes such as cars and villas to lure new customers.
While the Treasury is cool about lottery accounts, the Home Office, which supervises individual lotteries, is more open-minded. A spokesman said they could be legal: "Under the Lotteries and Amusement Act the setting up of lotteries for private profit or commercial undertakings is forbidden unless there is an element of skill or a free prize draw. If the societies also offer interest, it could be argued that the prize draw is free."