Research by Which? looked at all energy deals available and identified more than 70 fixed deals that were more expensive than the proposed energy price cap, which limits the amount that can be charged for certain elements of bills. The priciest of these was £1,332 a year for a medium user- £196 more than the average price cap of £1,136.

The cap, which is set to be introduced by the end of this year, will save households £75 a year on average according to Ofgem, though will only apply to default tariffs meaning those on expensive fixed tariffs won’t benefit from it.

Which? research found 98 energy tariffs which cost less than the proposed cap, with the cheapest deal costing £258 a year less for a medium energy user.

Medium energy users who are on the priciest Big Six standard default tariff would save £121 a year on average with the cap. But they could save £378 per year by switching to the cheapest available deal.

The energy price cap will be set at different levels around the country – depending on how much it costs to provide gas and electricity to a particular region.

The cap will be set at £1,124 in Southern Scotland, £12 lower than the UK average, and £1,154 in Northern Scotland, £18 higher than the UK average.

Of the Big Six suppliers, Ofgem figures show that Scottish Power customers could save the most under the cap, with medium energy users seeing their bills cut by an average of up to £121 a year.

Alex Neill, Which? managing director of home products and services, said: “While this cap may cut energy bills for some, people shouldn’t be lulled into a false sense of security that they are getting the best deal. As our research shows, the cap won’t cut everyone’s bills and you can save more by switching.

“The price cap is only a temporary fix, what is now needed is real reform to create competition, promote innovation and improve customer service.

“If you are unhappy with your current energy provider, you should look to switch now to another supplier and potentially save almost £400 a year.”