British Gas is compensating customers mis-sold energy tariffs £130 each on average, the company has revealed.
Affected customers signed up to a new energy tariff either in-store, via Sainsbury's Energy or at Westfield Shopping Centre and were given misleading estimates as to how much they could save by switching.
The face-to-face sales that overstated potential savings took place between February 2011 and March 2013 and account for 5% of such sales.
British Gas admitted that "in some cases customers were told that they would save money when in fact, it was more expensive to switch to Sainsbury's Energy or British Gas".
The Big Six energy supplier said it realised its mistake through its own internal checks and "took swift and decisive action to contact and compensate customers".
Regulator Ofgem was informed of the error and it has re-calculated the quotes of customers affected and "fully compensated" them.
Some 4,300 customers have received an average payment of around £130, including 1,300 customers who couldn't be reached but have had their accounts automatically refunded anyway.
British Gas said that a further 1,300 former customers could have been affected to the tune of £161,000. As it is unable to contact them, the company said it would donate the same sum to the British Gas Energy Trust.
Ian Peters, managing director of British Gas Residential, said: "We are very sorry and have ensured no customer will be out of pocket as a result."
Mark Todd, spokesperson for energy switching advice site Energyhelpline.com, said: "This is another sad chapter in the story of how poorly energy customers have been treated by their providers.
"It just goes to show how careful customers have to be when considering switching suppliers in face-to-face sales because the track record of doorstep or supermarket sales isn't good."
He added: "While it's understandable that it's very difficult to give an accurate projection of savings without a customer's energy bill to hand, it's not good enough for customers to be mis-sold to."
That said, he doesn't believe an outright ban on face-to-face energy sales to be necessary. "Customers can use such a meeting as a prompt to look into other deals available but they should go away and check an independent source."