Dermot Nolan, chief executive of Ofgem, told the BBC that domestic gas and electricity prices should be cheaper "for the vast majority of people".
Wholesale energy costs make up nearly half of a domestic bill, and have fallen by about a third in the last 12 to 18 months, he said.
Yet, prices had not fallen, he added.
Energy UK, which represents the major energy energy companies, insisted that there was a competitive market of 34 suppliers and that people should switch for savings of hundreds of pounds.
Lawrence Slade, chief executive of the trade body, said the industry had made "mistakes in the past" in failing to assist those languishing on variable deals but that the situation had improved alongside increased competition.
The regulator has said 70% of consumers remain on standard variable tariffs which have hardly changed since early last year.
Pressure is mounting on the UK's big six energy suppliers to cut their prices in line with falling costs after the latest analysis showed wholesale gas and electricity prices in the UK hit a five-year low at the end of 2015.
Figures published on Thursday showed the cost of energy on the wholesale market tumbled to Â£36.76 per megawatt hour on the Power Index, compiled by market information provider ICIS.

The 30-year-old has played 12 times for Orient since joining in October.
"There were one or two alternative options that came up but having been here for three months and got a feel for the place, I am happy to be staying," he told the club website.
Orient, who are 21st in League Two, face Mansfield on Saturday.

The alleged spying by the National Security Agency (NSA) "must be explained and more importantly new trust must be built up for the future", she told German MPs.
The allegations dominated the news during an EU summit last month.
Ms Merkel said the NSA affair was putting EU-US trade talks to the test.
She also said Germany's relations with the US "are of paramount importance".
The German government has said it is keen to hear directly from the fugitive NSA leaker Edward Snowden about the agency's collection of phone and internet data.
But Germany says it cannot offer him asylum because he would have to make his application on German soil.
According to his leaks, the NSA targeted communications among Washington's Western allies, including Ms Merkel's mobile phone and EU offices.
"The accusations are grave," Ms Merkel said in her statement on Monday. She did not comment specifically on the alleged bugging of her phone.
The Bundestag - Germany's lower house - is holding a special debate on the NSA spying allegations.
The scale of NSA surveillance in Germany is not clear, and last month Germany sent some senior officials to Washington to find out more.
German media report that the German secret services exchange intelligence with their US counterparts.
But recently the British newspaper the Independent, citing leaks from Mr Snowden, said the UK spy agency GCHQ had tapped into communications using a listening post on the roof of the British embassy in Berlin.
Mr Snowden, 30, fled to Russia in June after leaking details of far-reaching US espionage. He has temporary asylum, allowing him to live in Russia, until July 2014.
Energy companies are "overcharging in many cases" with bills failing to fall in line with dropping wholesale costs, the industry's regulator has said.
[NEXT_CONCEPT]
Leyton Orient midfielder Michael Collins has signed a new contract which will keep him with the League Two club until the end of the season.
[NEXT_CONCEPT]
Chancellor Angela Merkel has warned that reports of US spying in Germany - including bugging her mobile phone - are straining transatlantic ties.