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 boy was found unconscious and in cardiac arrest and was rushed to hospital where he died.
The victim, who was wearing her uniform at the time, was found knocking on doors nearly four hours after she was abducted.
There will be gales across Scotland and northern England this morning, but these will gradually ease through the afternoon.