Recently announced price cuts by the “Big Six” suppliers, which will all have come into effect later this month, will save customers on standard tariffs just £30 a year.
But Which? said the same customers could save up to £400 if they were to switch to the cheapest deal on the market, or £260 if they were on a gas-only tariff and switched to the lowest available deal.
The consumer group has urged the Competition and Markets Authority (CMA), which is due to conclude its investigation into the energy market, to make switching between providers and tariffs easier and impose penalties on those suppliers who do not protect the most vulnerable.
The remaining price cuts from the Big Six come into effect this month.
Government estimates suggest that just 12 per cent of customers currently switch their gas provider.
Which’s own figures suggest 71 per cent of gas customers are on standard tariffs and 88 per cent of households remain with the Big Six.
Its latest survey found 63 per cent of people are worried about energy prices and just a third (34 per cent) trust providers.
Which? announced it has submitted a dossier to the CMA with comments from more than 30,000 customers detailing dissatisfaction with energy companies and the market.
Which? executive director Richard Lloyd said: “Millions of people are still paying way over the odds for their energy, and levels of switching, while increasing, are still woefully low.
“We would urge all consumers, especially those on a standard tariff with the Big Six, to switch to a cheaper deal today.
“The stakes are high for the outcome of the energy market investigation and consumers will be expecting action to protect the most vulnerable and bring about fairer energy prices.”
UK Energy and Climate Change Secretary Amber Rudd said: “I have met the bosses of the Big Six and I have challenged them to bring down bills and pass on savings to consumers.
“All six have now dropped their prices, which is a step in the right direction and I will continue to champion the families and businesses who pay the bills and work hard to ensure they are kept as low as possible.”