Energy firm ScottishPower is to reduce dual-fuel prices by 3.3% from January 31 as it passes on savings from the Government's green levy shake-up.
The change will benefit 2.2 million households and reduce typical bills by around £42 to £1,199 a year for those paying by direct debit.
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There will also be a £12 rebate to all customers for the Warm Home Discount, which the Government has said will be funded through general taxation instead of through levies on energy bills.
The tariff cut will only partly reverse increases of 8.5% and 9% for gas and electricity respectively that ScottishPower hit customers with a month ago.
And 97% of customers on fixed-price products will not see their bills fall as the company said they were already protected from the rising cost of green levies.
The cut comes a week after Labour called on ScottishPower and rivals npower and SSE to immediately reduce prices for households after the Government cut the cost of the Energy Company Obligation and asked electricity distribution companies to take action to reduce network costs.
British Gas has already reduced prices in response, announcing in early December that it would cut bills by 3.2% on New Year's Day, scaling back hikes that saw prices go up by 10.4% for electricity and 8.4% for gas in November.
EDF and E.ON took the levy changes into account in the recent round of price rises, increasing tariffs on average by 3.9% and 3.7% respectively - far less than the increases announced by rivals.
SSE and npower are expected to follow ScottishPower by passing on levy savings. They have already committed to cutting bills, but have yet to confirm how much or when the changes would take effect.
Scottish Power said it would try to avoid any further price rises in 2014, but said this will depend on whether there are increases in wholesale energy prices or other costs outside of its control.