Consumer Focus is backing claims for an investigation into the big six energy firms not passing on wholesale savings to their customers.
The comments come after MPs called for a Competition Commission investigation into whether the firms are passing on price cuts in wholesale gas and electricity to the public.
Calls have been made in the past from Consumer Focus for energy suppliers to cut their costs and give their customers cheaper gas and electricity. It argues that customers are not getting a fair deal.
Robert Hammond, from Consumer Focus, said: "A truly competitive market would ensure that when energy companies pay less to supply energy, customers pay less to receive it. Yet none of the big six energy companies are breaking ranks and passing on lower wholesale costs to their mainstream customers."
Research conducted by the consumer group estimated that the price of gas and electricity could be reduced by 7.4 per cent and 3.1 per cent respectively based on prices in June 2009.
The Citizens Advice Bureau recommends that one way to reduce your energy bills is by comparing energy prices and switching gas and electricity supplier.
Click here to run an energy price comparison, and see if you could be paying less for your gas and electricity.