The poll found 33% of consumers are concerned about their energy bills but 43% do not make shopping around for a better deal a priority.
Almost half of British bill payers (45%) said they do not feel they could save much money and one in four (24%) said they thought shopping around for energy would be too much "hassle".
Previous studies found more than half of Britons (53%) say they are confused about energy tariffs.
But the regulator is launching the Be An Energy Shopper campaign in an effort to encourage consumers to take advantage of recent reforms to create a "simpler, clearer and fairer" energy market.
The campaign includes a consumer guide on the goenergyshopping.co.uk website to help people find the best energy tariff.
Ofgem chief executive Dermot Nolan said: "We shop and compare prices for many things in life, yet we often don't think to do the same when it comes to our energy bills, even when we could be saving around £200.
"With the introduction of Be An Energy Shopper it has never been easier to go energy shopping and get a better deal on your gas and electricity."
Energy Secretary Ed Davey said: "Making the switch is easier than ever before, and the Be An Energy Shopper campaign gives consumers practical advice on how to shop around and get the best deal for their energy use.
"Having made the switch myself, I would encourage anyone who hasn't already done so to check whether their current supplier is giving them the best deal -and if it isn't, switch.
"We're working to make the energy market work better for consumers.
"We want consumers to get the benefits of more competition."