Which? found that almost two-thirds of consumers (64%) are concerned about energy costs, a rise of eight percentage points since September.
More than a third of consumers (35%) do not trust the market, an increase of six percentage points.
The latest Which? findings come 30 days ahead of the watchdog’s deadline for energy companies to submit plans on how they can help their customers on the most expensive tariffs move to better deals, as part of its Fair Energy Prices campaign.
The consumer group said not one energy company had yet published a plan.
It said the temporary freezing of standard tariff prices by some suppliers did not go far enough to help customers on the most expensive deals.
Ofgem figures released last month showed around 66% of all households remain on standard variable tariffs, which are typically more expensive than fixed deals.
The regulator released the figure as it published the first league table comparing the most expensive standard tariffs with the cheapest deals on the market to provide greater transparency to consumers.
Which? found that, on average, customers with the Big Six could be saving up to £330 a year by moving to the cheapest dual fuel deal on the market this winter.
Alex Neill, managing director of Which? home and legal services, said: “The clock is ticking for energy companies, with 16 million households stuck on variable tariffs and trust in the industry falling. More needs to be done to move people onto better deals.
“With price hikes due later this year, temporary fixes from suppliers are just not enough to help people stuck on the most expensive deals.
“Energy companies will have no-one else to blame but themselves if the Government and the regulator have to step in and intervene.”