Thousands of families on Universal Credit or Pension Credit in Liverpool could save £300 on their heating bill if a proposed plan is implemented.
As the price of fuel soars, a one-off tax on energy giants could raise more than £5 billion for families in need.
Liverpool's Liberal Democrats wrote to Secretary of State for Energy Kwasi Kwarteng calling for him to back a so-called "Robin Hood tax".
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Kris Brown, the Liberal Democrat councillor for Woolton and Gateacre said: "It can't be right that a few energy firms are making millions from record gas prices while millions of people can't even afford to heat their homes as the cost of living crisis hits Liverpool hard.
"A one-off Robin Hood tax on gas and oil bosses would provide vital funding to support families in our area who are facing crippling energy price hikes.
"For years the Conservatives have ignored this problem and failed to take the bold action we need to reduce fuel poverty.
"The Government cannot look the other way any longer while families struggle to get by."
The Liberal Democrats also proposed the doubling of winter fuel allowance and the provision of funding to help insulate homes, cutting fuel bills in the long-run.
Some Conservatives are also calling on the government take action on soaring energy bills amid a spiralling cost-of-living crisis.
Liverpool-born Esther McVey, the former pensions secretary and the MP for Tatton in Cheshire, backed the demands of the Net Zero Scrutiny Group of Conservatives, made up of MPs sceptical of efforts to combat climate change.
In a letter to the Sunday Telegraph, they said: "The likelihood is that domestic tariffs will increase hugely, feeding directly into a cost-of-living crisis for many and pushing them into what is bluntly called ‘fuel poverty’."
This week, Tory MPs voted down a Labour Party proposal to cut VAT on energy bills, the Mirror reports.
Labour also wants to implement a windfall tax on North Sea oil and gas producers to help ease the squeeze on the cost of living with measures that would cut £200 from the average household energy bill.
