Martin Lewis' Money Saving Expert website had issued a stark warning for British Gas, Ovo, E.On and So customers.
Energy bills are set to fall by an average of 17% from next month and many firms are starting to offer fixed rates again for existing customers, the Mirror reports. Being on a fixed rate deal means you are protected if the Ofgem price cap rises again.
But if prices fall, you could be stuck paying a higher amount.