Some energy companies have been accused of "getting away with green murder" for failing to pass on savings from a Government shake-up of levies.
Just two of the "big six" providers, British Gas and Scottish and Southern Energy, have announced that they will pass on the savings - worth around £50 - to all customers, including those on fixed-price contracts.
Price comparison website Moneysupermarket.com said some bill-payers would be disappointed to learn that their supplier might not reduce the cost of their energy, mostly penalising those who were "savvy switchers" and already benefiting from a good-value fixed-price energy deal.
EDF Energy and E.On both said they took the Government's cuts to green levies into account when announcing their most recent smaller-than-expected price rises.
But both have said that existing customers on fixed price contracts will not benefit from the saving, claiming that they already benefit from a discounted rate.
Scottish Power has committed to passing on the proposed saving, but Moneysupermarket.com said this could also only apply it to variable rate standard customers based on the notes in a recent statement.
Chancellor George Osborne confirmed that the costs of some energy-efficiency and social schemes would be rolled back in last week's Autumn Statement.
Energy and Climate Change Secretary Ed Davey said the package would save households around £50 on average.
Moneysupermarket editor-in-chief Clare Francis said: "The reduction of green levy commitments for UK energy providers showed all the signs of being a good thing for struggling households who expected to see it reflected in their energy bills.
"However, indications are that not everyone will win in the war on the cost of energy and some will essentially lose out because they were savvy and switched to pay less in the first place.
"We feel this is unfair as these customers are in effect overpaying on the reduced levy whereas others are paying their fair share. Energy companies should evenly reduce the cost of green levies for all customers, and not have a selective approach as to who will get a reprieve. After all, the Big
Six blamed the Government levies to justify inflation busting price increases.
"For the many customers who signed up to a fixed tariff prior to the recent price rises to safeguard their household from the threat of rising prices, the green levy will have been built into the costs, and should now be reduced accordingly.
"Our advice to customers on fixed rate deals is to stay put as their existing tariff is still likely to be cheaper than the products currently available on the market. However, if you are on a fixed rate deal without any exit penalties, it is worth comparing prices once all of the changes take effect as there may be further savings to be made.
"Against a background of rising prices, £50 might be small but when times are tough every little helps. British Gas and SSE must be congratulated for taking this approach, and we would ask that all other providers do likewise."
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