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.
Ofgem said forward prices for gas and electricity had also fallen, and were around 16% and 9% lower respectively for the coming winter than last year.
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."
Which? executive director Richard Lloyd said: "The Big Six must now justify why falling wholesale prices have not yet had any impact on consumers' bills. The majority of consumers believe that suppliers put profits before customers, so there is still a huge job to do to rebuild trust.
"We'd expect to see the companies behaving fairly and passing on lower costs to their customers. Big changes are needed to fix the Big Six so it is now for the industry to respond."
British Gas managing director of residential energy, Ian Peters, said: "We buy our gas well in advance, so movements in wholesale prices, up or down, do not feed through immediately to retail prices. We have other costs that are rising - regulated transport and distribution costs, environmental costs, metering costs. We are certainly not increasing profits on the back of lower wholesale gas prices. Our trading statement last month downgraded profit expectations.
"The details of our hedging strategy are commercially sensitive. To disclose our hedging would risk tacit coordination which is not appropriate in a competitive market. So we will not comment on how we have reacted to specific events."
A spokeswoman for SSE said: "SSE announced in March a freeze on its household electricity and gas prices until at least January 2016. This is the longest price freeze the competitive energy market has ever seen and followed research among our customers which showed they were concerned about the prospect of rising energy bills over the next two years.
"Committing not to increase prices for such a long period of time requires a long-term view on costs. However we keep a close eye on all the costs that go into supplying energy, not just the wholesale cost, which accounts for one half of the bill - and if we can lower prices, we will."
Npower said: "We constantly monitor gas and electricity wholesale markets, with the aim to offer our customers competitive tariffs and protection from the volatility of said markets."
Energy UK, the trade association for the industry, said: " Wholesale energy is just one of a number of costs outside of an energy company's control, which make up a household bill. All energy suppliers aim to hold costs as low as possible for as long as possible. There are now 24 domestic energy retailers in the UK. They buy gas and electricity months and even years in advance to smooth out the swings in the market.
"When wholesale prices fall it can take time for bills to catch up as the gas and power may have been bought at a higher price some time ago.
"The suppliers also have to take all manner of risks and wider costs into account, including political and regulatory issues. The industry is committed to openness and will be answering the questions on wholesale prices to their customers and to the authorities.
"We would encourage customers concerned about their bill to contact their energy supplier and ensure they are on the cheapest tariff for their circumstances. The industry believes an honest conversation is needed about the way both gas and electricity prices are impacted by changes in the wholesale market. This year Energy UK has been publishing a regular wholesale electricity market report to ensure existing market information is readily available."
A spokeswoman for EDF Energy said: "We keep our prices under constant review and understand the importance of value to our customers. That's why our standard variable prices have been lower than our major rivals for 95 weeks out of 104 weeks over the last two years."
Gary Smith, national officer of the GMB said industry sources had told the union that wholesale electricity prices had fallen by 15%.
"In any normal market, price falls like this would have been passed on to the consumer. But there is no proper energy market in the UK, as this proves.
"Ofgem should be scrapped and replaced with a body which has teeth to make sure price falls are passed on to consumers."