Citizens Advice has called for energy firms to return £7.5bn in "unjustified profits" to consumers.
The charity says industry watchdog Ofgem could work with networks and suppliers to make sure customers get a refund, which would work out at about £285 per household.
A press release issued by Citizens Advice said Ofgem had allowed energy companies to make billions, without reflecting on how efficient they had been.
The statement said: "This would be similar to action taken by the water regulator Ofwat in 2013. Ofwat worked with water companies to return £435m of excess profits to consumers, out of a windfall of around £1.2bn over the course of their price control.
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Gillian Guy, Chief Executive of Citizens Advice, said: “Energy network firms are enjoying a multi-billion pound windfall at the expense of consumers.
“Decisions made by Ofgem have allowed gas and electricity network companies to make sky-high profits that we’ve found are not justified by their performance.
“Through their energy bills, it is consumers who have to pay the £7.5bn price for the regulator’s errors of judgment. We think it is right that energy network companies return this money to consumers through a rebate.
“If energy network companies fail to return these unjustified profits to the consumers that paid for them then the government should consider stepping in.”
In addition to asking for a rebate for consumers, Citizens Advice is calling for Ofgem to learn lessons and reduce costs for customers when designing the next price controls for energy networks.