As many as 2.1 million households have been hit by large late bills in the last year because energy suppliers initially undercharged them, according to estimates from Citizens Advice.
The charity made the estimate after its research among more than 2,000 people across Britain found that 10% had been back-billed - where energy firms send a revised bill after undercharging.
The average "catch up" bill was for £206 - but one in six (15%) people who had been back-billed said they were charged more than £250.
Citizens Advice has also seen cases where people have been back-billed for four-figure sums.
One person who asked the charity for help was billed out "of the blue" for £1,120, it said. Citizens Advice said the supplier had previously sent them estimated bills, had not read the meter over a five-year period and later demanded full repayment.
The charity also helped a blind man who set up a monthly direct debit because he could not take meter readings. It said three years later, he received a back-bill demanding £3,500 after the supplier said the monthly payment had been an underestimate.
Back-billing happens when customers have been undercharged for their energy for a period of time.
It can be because a customer did not pay a bill, but it can also be due to suppliers underestimating bills or not investigating a technical fault, Citizens Advice said.
Suppliers can back-bill a customer for up to 12 months worth of gas or electricity, even when it was the firm's fault. Customers can be back-billed for longer periods when the supplier argues the customer was at fault, the charity said.
Billing errors are the biggest energy problem people contact Citizens Advice's consumer service about, with 16,000 cases seen last year.
Gillian Guy, chief executive of Citizens Advice, said: "Customers shouldn't have to pay the price for suppliers' mistakes.
"Energy bills are already high so it adds insult to injury when companies go back to customers looking for more money after they got it wrong. Particularly for suppliers who insist on payment in full, this can be a huge burden on already stretched finances.
"Smart meters provide a perfect opportunity to consign back-billing to the history books. As they are rolled out across the country Ofgem should ensure suppliers reduce the length of time they can back-bill customers."
Energy Secretary Amber Rudd said: "This is very disappointing. I challenged the UK's biggest energy suppliers to bring down bills and pass on savings to consumers. They have dropped their prices which is a step in the right direction but errors on bills create unnecessary burdens and worry for hard-working people and I reiterate to all energy companies that they need to put their customers first and ensure that this does not happen.
"We're installing smart meters to help people take control of their energy use and bring an end to estimated bills, as part of our plan to build a system of energy infrastructure fit for the 21st century."