Campaign groups including Age Concern, National Energy Action and watchdog Consumer Focus were outraged after Ofgem unveiled the findings of its seven-month investigation.
It discovered 4.3 million customers were paying an extra £55 per year on average for electricity compared to customers who can access dual fuel rates.
Suppliers have been told to take action or face “onerous” regulations or referral to the Competition Commission.
The report said: “Many rural customers are not on the gas grid and thus are impacted by the higher margins earned on electricity consumers, but cannot benefit from lower margins on gas or the discounts available to dual fuel customers.
'This is compounded by higher heating costs (from the use of oil, electricity or liquefied petroleum gas), which drives a higher proportion of these customers towards fuel poverty.”
Alistair Buchanan, Ofgem chief executive, said investigators had found no evidence of a cartel, but had also raised concerns about charges to customers paying using prepayment meters or by cheque.
In total up to 12 million customers may be paying a higher rate than the best available deal.
Investigators also found a third of customers who switched deals did not secure a price reduction and this was nearly 50 per cent amongst prepayment customers, often the households most at risk of fuel poverty.
Mr Buchanan said: “I do not feel any discomfort in throwing the book at a company if we need to do that.
“There are still some players who are charging above a reasonable level and companies are not locking prices to their cost base.
“We have told the companies they have got to sort this out. If they do not, we will be looking for additional regulations or sending them to the Competition Commission.”
Ofgem has now launched a consultation on its findings, which will also put out feelers on Ofgem taking on additional powers due to the growing complexity of the energy market.
He said: “We want to look at whether there is an advantage to Ofgem taking on additional powers to give consumers confidence we can protect their interests.”
An Ofgem spokesman said this did not include at the moment taking on responsibility for off gas customers, although a parliamentary select committee suggested this earlier this year.
Ed Mayo, chief executive of Consumer Focus, said fuel poverty was “the main issue of this winter” and he was not afraid of “treading on the toes” of Ofgem if it did not do its job effectively.
He said: “Ofgem has gone some way to highlight action to bring about fairer pricing, but we remain concerned that there is a lack of true competition across the country.
“Ofgem should step up its work to bring more competition among the big six, encourage new entrants and increase trading or consumers will be at risk of not seeing sustained improvements.”