Residents in West Norfolk lost more than £11 million between them last year by not switching energy suppliers, according to industry campaigners.
The claim was made ahead of the launch of a new campaign next week which aims to encourage people to take steps to reduce their energy costs.
According to industry regulator Ofgem, residents can save around £300 on their annual energy costs simply by moving from one supplier to another.
But figures released this week showed that only 13 per cent of East Anglia residents switched their gas and electricity providers in the 12 months to July, one of the lowest figures in Britain.
It is also estimated that people are up to four times more likely to switch their home insurer than their energy supplier.
And officials from the Energy Saving Trust, which provides research on the industry, say more than 36,000 borough residents are on what it calls “Energy Autopilot.”
The term refers to people who believe they are on the cheapest energy tariff, but often are not.
Trust chief executive Philip Sellwood said: “Many bill payers in West Norfolk are missing out on substantial annual savings because they assume they are on the best tariff without actually checking.
“Prices fluctuate every year, so by not switching and being on Energy Autopilot, consumers may be sleepwalking towards having less money.”
The trust is working with Citizens Advice and the government to promote the benefits of switching providers during Big Energy Saving Week, which begins on Monday.
Events are being held across the country to encourage consumers to change suppliers before the winter.
However, no events are currently scheduled in West Norfolk, with the nearest to the borough taking place in Wisbech and Thetford.
Consumer minister Margot James said: “Millions of people have already switched and saved this year, but we know that some people can find it difficult to find the best deal.
“Big Energy Saving Week will help people up and down the country find out how they could save on their energy bills, as we create a country that works for everyone.”
Advice on how to switch companies, and how much you could save is also available at energycompare.citizensadvice.org.uk or via the Energy Saving Advice Service on 0300 1231234.