Ofgem has called on the Big Six energy suppliers to explain to their customers what impact falling wholesale prices will have on bills, saying the cost of both gas and electricity has been dropping "significantly" in recent months.
In a letter to the large suppliers, the energy regulator said their failure to engage with consumers on wholesale prices risked undermining public confidence and trust in the market.
Ofgem said that in early June gas prices for next day delivery reached their lowest level since September 2010 and were now around 38% below this time last year.
Prices for electricity reached their lowest level since April 2010 at the beginning of June, and were currently around 23% lower than this time last year.
Ofgem said that "as far as we know", the large suppliers had not explained the price drops to customers.
The regulator said that while there were upward pressures on energy costs from government schemes to support environmental objectives as well as network renewal, the costs of wholesale power and gas "dwarfed" these and made up just under half the total household bill.
The trend had been driven by the mild temperatures across Britain and Europe last winter, leaving gas storage at record levels.
The regulator said: "In a competitive market the threat of losing market share would encourage suppliers to reduce their customers' bills whenever there are sustained reductions in costs.
"Suppliers are yet to reduce their prices for existing customers to reflect the wholesale cost changes."
Ofgem chief executive Dermot Nolan said: "The Big Six suppliers tell us that they think the market is competitive, but our research shows that consumer trust is low.
"Therefore if suppliers are going to start rebuilding that relationship they need to take the initiative and explain clearly what impact falling wholesale energy costs will have on their pricing policies.
"If any of the companies fail to do this, consumers can vote with their feet. Independent suppliers are currently offering some of the cheapest tariffs on the market."
Ofgem is currently proposing referring the retail market to the Competition and Markets Authority (CMA) after a joint report with the Office of Fair Trading and the CMA confirmed that competition is not working as well as it could be.
A spokesman for the Department of Energy and Climate Change said: "Energy suppliers are responsible for their prices and must justify those prices to their customers. The best way to keep prices down is to introduce more competition, and our reforms have led to the number of suppliers trebling since 2010.
"People are switching in unprecedented numbers, and recent price cuts by some suppliers shows how competition benefits consumers. We also support Ofgem's proposal for a full investigation into competition in the energy market."