A group of local councils in England is formally asking the government for new powers to tax large supermarkets.
BBC News has learned that Derby City Council has called for the right to bring in a levy as a "modest" effort to ensure supermarket spending "re-circulates" in local communities.
Some 19 other local authorities back a so-called "Tesco tax" on big retailers, which could raise up to £400m a year.
The government said additional taxes on supermarkets would push up food prices.
A similar tax already operates in Northern Ireland and Scotland.
The council has made the suggestion under the Sustainable Communities Act, which allows communities and councils to put forward ideas to government to solve local problems.
In its submission, the council says that while supermarkets bring some benefits, they have an overall detrimental impact on the sustainability of local communities.
"Research has shown that 95% of all the money spent in any large supermarket leaves the local economy for good, compared to just 50% from local independent retailers; this levy is a modest attempt to ensure more of that money re-circulates within and continues to contribute to local jobs and local trade," its report states.
The council wants the right to impose a levy on large supermarkets, retain the money raised, and use it to help small businesses. It said it could also use the money to support community centres and parks.
The extra business rates levy, of up to 8.5%, would affect any large retail outlet with a rateable value of more than £500,000.
Ranjit Banwait, leader of the council, said communities in Scotland and Northern Ireland were "already benefiting" from the scheme.
"The revenue that we'll be able to generate will mean that we can support local businesses - especially small businesses," he said.
"We'll be able to improve public services."
The government will have six months to respond. If agreed, the levy would apply not just to the 20 councils seeking change but to all local authorities in England.
And if every one of them took it up, it could cost the big supermarkets alone an extra £190m in tax.
If the levy was imposed on all big out-of-town retailers, including businesses such as Ikea, Homebase and B&Q, it could raise about £400m in total.
But the government has already given an indication of how the idea will be received.
The move would hit low-income families the hardest, said the Department for Communities and Local Government (DCLG).
"We ruled out such a bid for higher taxes under the last round of the Sustainable Communities Act proposals," it said.
"There are much better ways to support small shops."
However, the move has been given a cautious welcome by the former retail boss and High Street campaigner Bill Grimsey. He proposed the idea of a levy in his independent review of the High Street last year.
He called for a one-off levy on retailers and pub groups with a turnover of more than £10m to help finance plans to allow struggling town centres to rebuild themselves for the future.
Mr Grimsey said it was right that the biggest retailers put something back into their high streets:
"Used wisely, it could leave a lasting and powerful legacy. But I don't want this introduced as an annual levy that essentially becomes another tax," he said.
"If it's used simply to plug council budget shortfalls, it won't be fair and it'll be anti-business. This has to be about the High Street, not clobbering big business."
Town centre expert Mark Williams said the current rates system would be better than a supermarket levy at improving town centres.
"Ironically supermarkets are not looking to go out of town. Customers don't like them - those big starships that landed in those green areas - they are now being cancelled and we are now seeing announcements by Tesco to convert sites that they've got into residential [developments]."
Supporters of the move, which include Oxford, Brighton and Hove, Preston, Southwark and Sefton councils, believe the supermarkets can afford it, saying it is just a fraction of the costs that supermarkets had to swallow when VAT was raised in 2011.
But retailers are likely to strongly resist the move arguing that they are taxed enough already. They pay more in business rates, a property-based tax, than any other form of taxation and have been urging the government for a complete rethink on the system.
They will also raise concerns about fresh investment and jobs being put at risk.
The British Retail Consortium has said it is consulting its members on the proposed tax.
The levy imposed by the Scottish government on larger shops selling alcohol and tobacco is set to end next year. The aim of the scheme was to make them contribute to public health measures.
It is clear Derby City Council's idea for an additional tax on retailers south of the border will spark even more heated debate.