More than 13 million British households missed out on savings last year because they did not change their energy supplier, with almost 60% of them believing they were on the cheapest tariff available, the poll to mark Big Energy Saving Week found.
The campaign group said it was unlikely this was accurate, noting that just 30% of all bill payers believe energy suppliers actively encourage customer loyalty.
In contrast, 24% of households have switched home insurer at least four times in the last 10 years.
The national campaign, run by the Energy Saving Trust, Citizens Advice and the Department for Business, Energy and Industrial Strategy (BEIS), aims to encourage consumers to switch and help them access the financial support they are entitled to.
Energy Saving Trust chief executive Philip Sellwood said: "Many bill payers 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."
Consumers 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, many could save around £300, as we create a country that works for everyone."
- Ipsos Mori surveyed 2,480 adult bill-payers in September.