Customers have seen big increases in gas and electricity prices
Prime Minister Gordon Brown is facing mounting pressure from Labour MPs for a one-off windfall tax on energy firms which have recorded huge profits.
More than 80, some of them ministerial aides, say the money should go towards helping poor families pay energy bills.
Meanwhile, council leaders are calling for an annual levy to fund a home insulation programme.
The government says it is looking at a range of options. Energy firms warned a profits "raid" could put off investors.
The prime minister's spokesman said: "The position on tax is a matter for the chancellor and the Treasury. The Treasury receives a whole range of representations and of course will consider such representations in the normal way."
Seventy five Labour MPs have publicly signed the Compass petition but the left-leaning think tank says there are more than 80 - as some chose to remain anonymous.
Among signatories are Stephen Pound, aide to welfare minister Stephen Timms, and Rob Marris, aide to Northern Ireland Secretary Shaun Woodward, who suggested to the Times that he would consider quitting if there was no change in policy.
But the prime minister's spokesman said: "What matters is the view of Treasury ministers. They are not ministers."
While a windfall tax has not been ruled out, it is understood the prime minister is looking at an alternative levy on carbon emissions.
Labour MP Clive Betts told BBC Radio 4's Today programme there was "overwhelming" support for a one-off tax among his parliamentary colleagues and the public.
He said companies were looking at more than 30% increases in their profits, adding: "They are simply going to make much more money for doing absolutely nothing."
But David Porter, chief executive of the Association of Electricity Producers, said a windfall tax on firms' profits could break the trust between government and industry and mean more investors head abroad.
He said firms had to invest £100bn in new power stations over the next 11 years adding: "A legalised raid on the company's bank accounts - that would be very unhelpful because it would scare off investors and also could make the cost of investment much higher and, in the end, that would end up on the customers' bills."
The LGA, which represents councils in England and Wales, has written to the government asking for a yearly levy to fund an insulation scheme, which they say would be more effective than a one-off payment.
The leaders of Conservative, Labour, Liberal Democrat and independent groups at the LGA have written to six cabinet ministers to make their case.
Labour MP Lindsay Hoyle has also started a Commons motion calling for a windfall levy on energy companies to be used to boost the winter fuel payment for pensioners. It was signed by 38 MPs, before they left for summer recess.
He told the BBC a windfall tax would be a way to curb "immoral" profits and there was "nothing new in it" as it had been used by Labour and previous Conservative governments to control profits.
When Labour came to power in 1997 it imposed a windfall tax on utility companies - privatised under the Conservatives - to fund the welfare-to-work New Deal programme. But that tax had been announced in the party's manifesto.
Ruth Lea, an economics adviser to the Arbuthnot Banking Group, said the firms already paid a large amount of tax on their profits and had to pay a dividend to their shareholders.
"To have these arbitrary retrospective taxation moves is a mistake and it will put off investors," she added.
The "big three" energy firms - Shell, BP and British Gas - have recently posted substantial profits.
Shell made £4bn in the second quarter of this year, up 4.6% from 2007, while BP made £3.4bn, a rise of 6%.
Centrica, which owns British Gas, made £992m in the first half of this year, while raising prices for customers by 35%.