British Gas and E.on are freezing the price of their standard variable tariffs until at least the end of March 2017, hot on the heels of a similar move by rival supplier SSE last month.

Centrica-owned British Gas is the UK's biggest energy supplier, serving about 11 million households – six million of whom are on its standard tariff.

The firm, which announced its price freeze today via adverts in national newspapers, said the move would "help bring some peace of mind" to those six million customers.

E.on followed suit this afternoon by freezing prices on its own standard variable tariff, called E.on EnergyPlan, saying it was "pleased to be able to offer that reassurance to our customers".

The majority of E.on's 4.6 million customers are on its standard tariff, understands.

In November SSE promised not to raise prices on its own standard tariff until at least April 2017. The announcements come as wholesale energy prices – what energy firms pay for gas and electricity – continue to rise, with smaller suppliers such as Ovo and Co-op Energy cranking up prices in recent weeks. On Saturday small firm GB Energy went bust after struggling to cope with changing market conditions.

Despite the recent price freezes, standard variable tariffs remain among the most expensive deals for energy customers. British Gas's standard tariff costs dual-fuel households £1,044/year based on regulator Ofgem's typical usage figures, and E.on's costs £1,047/year.

However, British Gas customers can save over £40 a year just by switching to its HomeEnergy FreeTime Mar 2018 tariff, according to the firm's own figures. A typical dual-fuel household would pay £1,001/year on that tariff.

E.on customers can save £32 by moving to its cheapest Energy Fixed 1 Year v20 tariff, typically costing £1,015/year.

But if you're an E.on or British Gas customer who's willing to switch suppliers, the cheapest deal on the market is currently £863/year for a typical dual-fuel home, from small provider Places for People. And with energy prices likely to keep rising next year, the savings you'll potentially make through switching now could be considerable.

MoneySavingExpert's main message is that comparing tariffs is the only way to ensure you've got the cheapest deal. You can find the best tariff for your household using our free Cheap Energy Club comparison tool.

'Switching NOW could save you £180 a year'

Commenting on the British Gas announcement this morning, MoneySavingExpert founder Martin Lewis said: "Don't let these price freezes by British Gas, E.on, SSE or any others who announce similar, lull you into a false sense of security.

"If you are on a standard tariff from a big six firm, you are already massively overpaying. For someone with typical use, you're paying £1,060 a year. If you're willing to change company, the savings are getting on to £200 a year at typical usage, and much more for many customers who have bigger bills. And those tariffs are fixed for one year, so they're cheaper, and you're locked in with a guarantee of no hikes for far longer.

"The reason these firms feel the need to promise a price freeze is because the huge increase in wholesale prices and the weakness of the pound means we're seeing massive inflation in the energy market. So this is almost certainly just delaying the misery of price rises.

"Come the end of winter, expect to see hikes of up to 10% by many of the big six companies. And in fact, most of the big six firms have been quietly removing the cheapest deals from the market – stealth price rises.

"So let me shout it again – the most important message is not 'don't act', it's 'act now', because we've already seen the market's cheapest deals rise by £150 a year for someone on typical usage as cheap deals are pulled."