Energy Secretary Ed Davey said he wants to bring Ofgem in line with other regulators such as Ofcom and the Financial Services Authority, who can ensure compensation goes to customers.
Currently energy suppliers voluntarily give cash to consumers following errors - but there is no obligation - while Ofgem has been able to fine companies, but that money has gone to the Government.
The redress could include pound-for-pound compensation, goodwill payments or public apologies.
More top news
The death toll following the collapse of a six-storey building in Nairobi rises to 10 as fears grow for those still trapped in the rubble.
Springwatch presenter Chris Packham describes his battle with depression as "great, hopeless vacuum".
A newly promoted police officer caused a sensation with local women on Facebook