The anonymous group Don’t Pay UK said that if enough households commit to a “mass non-payment” on October 1, the regulator Ofgem will abandon plans to lift the price cap.
The latest predictions suggest Ofgem will push the cap on household energy bills up to around £3,450. It will then update the cap every three months, rather than every six.
Citizens Advice has warned people they could be charged a fee to cancel their direct debits and then have to pay higher monthly payments.
Customers who miss several payments can also be moved onto a more expensive prepayment metre or, in some cases, be disconnected.
A Government spokesman said: “This is highly irresponsible messaging, which ultimately will only push up prices for everyone else and affect personal credit ratings.
“While no Government can control global gas prices, we are providing £37 billion of help for households including the £400 discount on energy bills.”
Energy UK, which represents suppliers in the UK, said bills have reached a record high because Russia’s war in Ukraine has disrupted gas supplies and caused wholesale prices to soar.
A spokeswoman added: “Suppliers need to be able to cover the costs of buying energy otherwise we could see even more of them go out of business.
“Thirty suppliers have exited the market since last August which Citizens Advice recently estimated could add £4.6 billion to customers’ bills.
“Any customer who is struggling to afford their energy bills should contact their supplier to see what assistance might be available.”
In a statement on its website, Don’t Pay UK said it is “demanding a reduction of energy bills to an affordable level”.
It said: “Our leverage is that we will gather a million people to pledge not to pay if the Government goes ahead with another massive hike on October 1.
“Mass non-payment is not a new idea, it happened in the UK in the late 80s and 90s, when more than 17 million people refused to pay the Poll Tax.”
It added: “Even if a fraction of those of us who are paying by direct debit stop our payments, it will be enough to put energy companies in serious trouble, and they know this. We want to bring them to the table and force them to end this crisis.”