Prime Minister Andy Burnham has asked ministers to develop a plan to remove standing charges from gas bills.
These are fixed daily fees that cover the costs of connecting to a supply. They vary by region and households must still pay them even when energy is not being used.
Industry body Energy UK said whether the proposed changes would make a difference to bills would depend on how or where the charges were reallocated on the bill.
But an influential research foundation argued it would be a progressive move that would help those on low-incomes and knock £27 off a typical annual bill.
During Prime Minister's Questions, Burnham said the "pragmatic decision" on giving the green light to the Jackdaw gas field in the North Sea would allow the government to increase investment in renewables and "do more to help people with bills".