Consumer group Which? said recent reductions to energy bills should be twice the size of the concessions on offer and should have come a lot sooner.
Which? said the "big six" energy firms, which together supply 95% of consumers, should be reducing prices by up to 10.3%.
The consumer body says that energy firms have failed to align retail prices with wholesale gas prices. Meanwhile, energy has cost consumers £2.9bn over the last year, or about £145 per household.
Which? executive director Richard Lloyd said: "Our analysis places a massive question mark over how suppliers have been setting prices over the last two years.
"They now need to explain to their customers why bills don't fall further in response to dropping wholesale prices. Energy bills are consistently the top consumer concern so it's about time people got a fair deal."
Npower, British Gas, E.On, Scottish Power and SSE recently announced that they will be reducing bills by between 3.5% and 5%. EDF Energy will reduce prices by 1.3%. Meanwhile, wholesale gas prices have fallen by 20% since the start of December 2014.
The consumer body says that energy firms have failed to align retail prices with wholesale gas prices, which have cost consumers £2.9bn over the last year - £145 per household.
Which? says that it has submitted the findings of its research to the Competition and Markets Authority.
"While the competition inquiry should establish beyond doubt whether the price people are paying today is right, consumers will now look to politicians of every party to set out how they'll deliver fair and affordable energy prices in the future," added Lloyd.