The Local Government Association was responding to the latest round of profits announced in the city by the leading energy companies.
They include Centrica, the parent company of British Gas which has posted half-year profits of£992m.
Paul Bettison, who chairs the LGA Environment Board, said: "Energy companies are making massive profits at the expense of hard working families.
"If these firms paid the same as householders do through their bills we could insulate 10 million homes, take£2bn off energy bills and lift 500,000 people out of fuel poverty.
Cllr Bettison said the cut in bills would be the equivalent of a penny off the standard rate of income tax and would help people to manage rising costs.
He added: "Meeting this country's ambitious targets to reduce carbon emissions and help households manage rising fuel costs will require ambitious policies.
"We should seize the chance to pay for a massive investment drive to insulate people's homes that provides a long term solution to rising fuel costs and cutting carbon emissions."
This week the Local Government Chronicle (LGCplus article) reported that 30 councils were forming a consortium to consider bulk-buying oil of the world's financial markets.