Britain's under-fire energy suppliers have said they will cut household bills after the government confirmed a shakeup of green levies.

British Gas said it would reduce gas and electricity prices by an average of 3.2%, equivalent to £41 from an annual dual-fuel bill, with an extra £12 rebate for the government's warm home discount scheme.

Its rival Scottish & Southern Energy said it expected a saving for the typical dual-fuel customer of around 4% before the end of March, equivalent to a saving of around £50.

The moves come after the chancellor, George Osborne, confirmed that the costs of some energy-efficiency schemes would be rolled back in this week's autumn statement.

Npower said it did not plan to increase energy prices before spring 2015 unless there were increases in wholesale energy costs or network charges.

The cut in British Gas bills comes two weeks after it raised electricity prices by 10.4% and gas tariffs by 8.4%, adding around £123 to the average annual bill.

British Gas's managing director, Chris Weston, said on Monday: "British Gas is pleased to be cutting energy bills by an average of £53 from 1 January.

"We have been able to do this because the government has committed to making changes to the environmental and social obligations that are paid for through energy bills. These changes will now allow us to help more people at a lower cost."

The government is cutting the cost of the energy company obligation (Eco), an insulation scheme delivered by major energy suppliers, in a move that should shave £30-£35 off bills, on average, next year.

The Department of Energy and Climate Change also announced it was establishing a rebate, saving the average customer £12 on their bill for the next two years.

Electricity companies will also take voluntary action to reduce network costs in 2014-15, funding a one-off reduction of around £5 on electricity bills.

The energy and climate change secretary, Ed Davey, said: "Energy bills are a big concern for many people, which is why we've been working to reform the energy market, increase competition and make it easier for people to shop around and switch supplier.

"Today's announcement confirms a serious, workable package which would save households around £50 on average."