Just two of the "big six" providers, British Gas and Scottish and Southern Energy, have said 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 households would be upset to learn their supplier might not cut bills, mostly penalising those who were "savvy switchers" 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. Both say existing customers on fixed price contracts will not benefit from the saving, claiming they already benefit from a discounted rate.
ScottishPower has committed to passing on the saving, but Moneysupermarket.com said this will only apply to variable rate standard customers based on notes in a recent statement.
Npower has so far said that it does not expect to raise prices again until 2015.
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 £50 on average.
Moneysupermarket editor-in-chief Clare Francis said: "Energy companies should evenly reduce the cost of green levies for all customers."