Energy suppliers are to refund customers on up to 1.5 million pre-payment gas meters after a fault led to "over-collection".
Trade association Energy UK said suppliers will be contacting every affected customer and will refund any money owed "as quickly as possible".
It said the problem came about because up to 1.5 million meters did not work properly when they were installed, adding that suppliers "know who is affected and have a solution".
Energy UK said in a statement: "As soon as the issue came to light companies began work to fix it and arrange refunds.
"In some cases a customer's meter will have already been fixed as programmes get under way across the country. All the companies involved will be working over the coming months to get round everyone who is affected."
Pre-payment meters use a calorific value (CV) code to calculate the amount of gas to be charged for.
But the fault meant the CV for some meters was not set properly, resulting in inaccurate readings.
Energy UK said affected meters would be fixed in a roll-out starting today, and the first of the refunds were expected to be given out before Christmas.
It said the industry recognised the distress this could cause and was working "as fast as it can" to resolve the problem, adding that the amounts were "very small, and most top ups will not have been out by more than 25 pence".
Angela Knight, chief executive of Energy UK, said: "Suppliers are working hard to roll out a solution for an issue which has affected some pre-payment gas meters.
"The meters were manufactured with a problem where they over-collected from customers. However, the companies know who is affected and will be getting in touch directly to put the meters right and refund any money owed.
"The suppliers and the wider industry are all very sorry this problem has occurred but are already getting in contact with customers. Customers do not need to do anything - their supplier will get in touch but, if they are concerned, they just need to contact their energy company who will be able to help."
Which? executive director Richard Lloyd said: "This is yet another shameful example of energy companies failing their customers and one that has hit some of the very people who can afford it least.
"Suppliers need to fix this fault as soon as possible and fully reimburse - with interest - the hundreds of thousands of people who have been overcharged.
"We urgently need major reforms to fix this market and increase the low levels of trust we consistently see in energy firms."
Ofgem senior partner for markets Rachel Fletcher said: " We are determined that no consumer should lose out because some energy suppliers have overcharged some consumers on pre-payment meters.
"By the end of this week we expect industry to come forward with a swift timetable for resolving all traceable cases of over-charging customers, repay consumers within a clearly-agreed and publicly-announced timetable, reconfigure meters as quickly as possible and protect customers from over-payment in the meantime.
"Suppliers must act quickly to resolve the problem in a way that treats customers fairly. We have not ruled out enforcement action."
Citizens Advice chief executive Gillian Guy said: "Prepayment meter customers are footing the bill for energy firms' errors. That overcharging has been going on for seven years shows the second-class service prepayment customers get. Prepayment meter customers are already paying higher charges than direct debit customers, so this is adding insult to injury.
"As a minimum customers now have a right to expect a refund on the mistaken extra charges and any interest on this money. Faulty meters that overcharge them are just the tip of the iceberg when it comes to problems experienced by prepayment customers. It costs prepay customers £80 more a year to heat and light their home, just because they use a prepayment meter.
"As it stands many people are only able to top up their meters by going to a local shop. This often means that people who are housebound or those with children at home have to go without heating or lighting, until they are in a position to leave the house or get someone to go for them. Energy companies need to make topping up their gas and electricity meters easier, including allowing people to top up over the internet or by phone."
Shadow energy secretary Caroline Flint said: " Pre-payment meters are often a last resort for people struggling to manage their energy bills or in debt to their energy supply. These customers can ill afford to be paying for energy they haven't even used.
"This is the latest example of an energy market that is not working in customers' interests. That's why the next Labour government will freeze energy prices until 2017, reform the energy market and create a tough new regulator with the power to strip energy companies of their licences if they repeatedly mistreat customers."