UK energy companies have been told to pass on savings to consumers cutting back their usage.
Business Secretary Grant Shapps said he was disturbed by reports of bills going up despite customers trying to be frugal.
This can happen if suppliers overestimate usage from households who pay a monthly direct debit.
In a letter to suppliers, Mr Shapps told them to explain how they would prevent this from happening.
“It is in all our interests that when consumers take sensible steps to reduce their own bills, such as reducing their boiler flow temperature or making their homes more energy efficient, that they are able to see an impact in their bills,” Mr Shapps wrote.
“I am very keen that all suppliers find a way to make their systems more responsive to these positive changes in consumer behaviour.”
Household energy bills are up by 27 per cent amid a gas squeeze blamed by ministers on Russia’s invasion of Ukraine.
Unlike many European countries, Britain has set no formal targets for households to cut demand.
But an energy campaign is believed to be in the works in which people will be urged to turn thermostats down by 2ºC this winter.
Mr Shapps said some consumers were making “huge efforts to reduce their usage to save money at a time when household incomes are squeezed”.
A freeze on energy bills at a typical £2,500 ($3,020) per year until April is expected to cost the government about £38 billion ($45.95bn).
As ministers try to increase long-term energy supplies, a row is brewing among Conservative MPs over whether to turn to onshore wind farms.
Mr Sunak promised to block onshore wind in the summer leadership campaign, in a play to the party’s homeowning base.
A former minister in both their governments, Simon Clarke, wants to amend a regional development bill to lift a ban on onshore wind.
“If you want to know why we should have more renewables, just look at your gas or electricity bill,” former party chairman Jake Berry told the BBC’s Sunday with Laura Kuenssberg programme.
The opposition Labour Party has signalled it could back the amendment to pile pressure on Mr Sunak.
The Prime Minister has also reinstated a ban on fracking, after Ms Truss briefly moved to resume shale gas extraction.