The Government recently announced that it was rolling back the green levy on energy firms in a move expected to save households around £50 a year.

However, only two of the “Big Six” providers, British Gas and SSE, have said that they will pass on the benefit to all customers.

EDF Energy and E.ON have both said their smaller-than-expected price rises (3.9% and 3.5% respectively) will only impact those on variable priced tariffs. Existing customers on fixed deals will not benefit from the Government reduction.

Scottish Power has committed to passing on the amount that the Government proposed but could also only apply it to variable rate standard customers based on the notes in a recent statement.

npower, the energy company which passed on the biggest autumn price hike – 10.4%- making its standard priced energy bills the most expensive in the UK, has said that it does not expect to have to raise prices again until 2015, matching the promise made by EDF Energy. It has said it will be reviewing the current price increase to see if these could be reduced, but again this will only apply to variable tariff customers.

Clare Francis, editor-in-chief at MoneySuperMarket, said: “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.”