The website claims that the Department for Work and Pensions (DWP) posted out letters to people likely to be eligible for Winter Fuel Payments, many of whom will be vulnerable.

The letters featured what MSE says is “incorrect and financially damaging wording” on the reverse of the envelopes that encourages switching energy tariff to save “an extra £290”. People were then told to contact Citizens Advice for more information.

But people who switch energy tariff now could be lured into expensive fixed rate tariffs that will cost them more than they are paying now. Whereas those who do nothing will either be on, or eventually be moved to, their provider’s default standard variable tariff, and be protected by the energy price cap.

The DWP wouldn’t confirm how many envelopes had already been sent out, but insists it will keep sending them with the same wording despite being contacted by MSE about the error. It said the envelope batch was “created before the rise in energy prices” and would have been “impractical, costly and wasteful” to replace.

Martin Lewis, founder of MoneySavingExpert.com, said: “We are in an extreme energy bill crisis. The logic of how to manage bills has been turned on its head. There has never been a time when clarity of message and action is more important. That’s why the government mailing out an incorrect message to millions of people, including many of the nation’s most vulnerable, is too big a risk to take.

“The right move for most people right now is to do nothing – don’t switch. That’s because if you do nothing, you’ll either be on, or automatically moved to your provider’s default standard variable tariff, which is priced capped. The price cap forces energy firms to sell energy at below its cost price – there is no meaningfully cheaper option.

“Due to the obvious hit to their finances, many big energy providers are trying to persuade people to move off those tariffs to fixed deals at premiums often far higher than 30%. They are using all the marketing tricks in the book to do it, and playing on the fact that until now that has been the right option. This is why this back of the envelope message, which seems to confirm that switching is the right move, is so dangerous – it adds a halo to the message from the energy firms to get people to switch.”