However, it said energy firms could do more to make sure that all customers were able to access the best tariffs.
"Initial findings from our energy market probe give us grounds to demand that companies end practices that hinder customers, especially the vulnerable, from getting the best deal," said Ofgem chief executive Alistair Buchanan.
"If they fail to satisfy our requirements voluntarily, then we can move to a Competition Commission reference," he added.
There has been widespread criticism of the billing system for customers on pre-payment meters, who are charged more for their fuel than those who pay by direct debit.
The average annual bill for households on pre-payment meters was £118 higher than those who pay by direct debit following the latest round of price increases.
Those who pay by cash or cheque each quarter - standard credit - pay about £80 a year more than those on direct debit. This is the most common form of payment for the fuel poor, as more than half of this group pay in this way.
"Ofgem's proposals to improve the market are welcome, particularly if these lead to the banning of price differences for pre-payment customers and those that pay by cash or cheque," said Gordon Lishman, director general of Age Concern.
"However, much wider reforms are needed. It is particularly vital that social tariffs are made fit for purpose, and are made mandatory through legislation, so that the poorest consumers get the cheapest energy rates."
Ed Mayo, of watchdog Consumer Focus, told the BBC that the report was a "devastating critique" of the treatment of older and vulnerable customers.
He said that customers were not getting the best deals when they switched suppliers.
This should be sorted out, he said, even if the report told consumers that they would have to put up with high bills.
Last week, government figures showed that fuel poverty in the UK rose to 3.5 million in 2006, one million more than in 2005.
Fuel poverty is defined as households who spend more than 10% of their income on fuel.
David Porter, the chief executive of the Association of Electricity Producers, said that the UK could do little about rising bills because coal and gas prices were globally driven.
Garry Felgate, chief executive of the Energy Retail Association, which represents suppliers, said: "Ofgem found no evidence of an energy cartel, and confirmed that the British energy market remains one of the most competitive in the world.
"Our priority over the next two months is to work with Ofgem to ensure that the market continues to work in the best interests of all consumers."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.