The biggest companies add a surcharge to the tariffs of customers that they inherited from their time as monopoly suppliers, meaning that these households pay more for their energy than they need to, the think-tank IPPR claimed.
The IPPR's analysis found electricity bills in 2013 for customers who had not switched supplier since the market was opened to competition were on average £27 higher than for customers who had switched.
Gas bills in 2013 for those who had not switched supplier were on average £76 higher than for customers who had switched.
IPPR senior research fellow Reg Platt said: "Competition is failing in the energy markets. Our new analysis shows how the biggest energy companies add a surcharge to the tariffs of customers that they inherited from their time as monopoly suppliers.
"Ofgem has shown itself to be incapable of taking the action that is necessary to get the energy market working in the interests of consumers. It's time that the market was reformed so that small energy service companies, local authorities, communities and individuals can all become active players."
An Ofgem spokesman said it was "wrong" for the IPPR to suggest the watchdog had not tackled the issue.
He said: "Our reforms for a simpler, fairer market address this as since the end of December 2013 all suppliers have been restricted to offering just four tariffs per fuel. They must also ensure that they offer the same deals to new and existing customers. Our reforms make it far easier for consumers to compare offers and find the best deal for them."