Consumer groups called for immediate cuts in energy bills following the announcement that British Gas profits had jumped 58%.
Philip Cullum, deputy chief executive of Consumer Focus, said there are "no excuses" for not reducing tariffs and claimed the market is in need of "fundamental reform".
The GMB union said the Government should intervene to help those struggling to pay.
The calls came after Centrica revealed its British Gas residential arm made profits of £595 million last year - up 58% on 2008.
Mr Cullum said: "Energy companies have no excuses for not cutting bills for their customers. It is clear the problems in the energy market are profound and that it requires fundamental reform.
"For consumers, a combination of high prices and cold weather has exacted a heavy cost. Energy companies have taken advantage this winter, while more than six million UK households live in fuel poverty and face a desperate struggle to keep warm.
"That British Gas has been the only major energy supplier to cut standard prices over the past seven months demonstrates a market largely devoid of competitive pressure. Energy companies seem not to care about providing value for money."
Gary Smith, GMB national secretary for energy, said: "GMB is asking the Government to look at redirecting some of these excessive profits back to the most vulnerable and needy energy users in our society. There should be lower tariffs for these consumers."
Centrica, which revealed a 7% drop in total group underlying operating profits to £1.86 billion as declines in wholesale gas prices saw dwindling returns from its upstream production business, said it realised 2009 was a "difficult year for many of our customers".
The group also warned that wholesale prices are forecast to rise again during 2010, although not to levels seen during the oil price bubble in 2008.