The ESB has come in for criticism for not passing on more cuts to the public despite profits of more than €600m last year.
The cost of both wholesale gas and oil collapsed in 2015, but customer prices have fallen by only 4%.
Consumer groups want the energy regulator to intervene and ensure that savings are reflected in bills.
Managing Director of Bonkers.ie, David Kerr, has said people still need to shop around: “The regulator has worked extremely hard to get out of price setting.
“So they no longer set the price for gas or electricity, the average customer will save €376 per year on their gas and electricity, just by shopping around.
“And the competition is absolutely fierce right now, these are the biggest percentage discounts we have ever seen.”