Just a third of consumers are able to choose the cheapest energy deal despite the introduction of simplified tariffs, according to a watchdog.
Which? said Ofgem's new rules for standardised tariffs were "a step in the right direction" but found that two-thirds of consumers still failed to identify the cheapest deal.
The consumer group challenged people to spot the best deal using the standard tariffs of the big six energy suppliers - British Gas, EDF, E.ON, Npower, Scottish Power and SSE.
It found that a third (35%) chose correctly when tariffs were presented in line with Ofgem's new Retail Market Review (RMR) structure, made up of a unit rate and standing charge.
Of the rest, three in 10 (31%) picked the wrong tariff and a third (34%) either did not think it was possible to calculate or did not know how to.
Four in 10 (41%) used an aid to do their calculations such as a calculator or spreadsheet, yet only 50% of these people got it right.
Which? said the results were an improvement on a similar test in 2012, when only 8% could pick the cheapest deal using the old-style energy tariffs, "so while the RMR structure is an improvement, our latest results show that the majority of people are still baffled".
Alongside the RMR structure, Ofgem is bringing in a new system of presenting energy tariffs called the Tariff Comparison Rate (TCR), which displays tariffs based on what a medium energy user would pay and is intended to prompt a hunt for cheaper deals by low and high users.
Which? found that only 8% of those surveyed found the TCR display easy to understand.
When asked to pick the cheapest deal for low users, nearly two-thirds (64%) chose the supplier with the lowest TCR figure - which would not have provided the best deal as there is no way of working that out using the TCR.
The watchdog said it was concerned that TCRs were likely to appear in advertising and on comparison sites, leaving some consumers worse off by incorrectly using them to compare and decide on a new tariff.
Which? is running a Fix The Big Six campaign, calling on the Government, Ofgem, competition authorities and energy companies to drive forward reforms to fix what it calls a "broken" market.
Which? executive director Richard Lloyd said: "In spite of Ofgem's tariff reforms to simplify the market, consumers are still failing to spot the cheapest deal because energy pricing remains too complicated.
"More radical changes are needed to fix the broken energy market.
"That's why our FixThe Big Six campaign is also calling for a full competition inquiry, so that hard-pressed consumers can be confident that the market works well for them as well as shareholders, and that the price they pay is fair."
Trade association Energy UK said: "Energy companies have made great changes helping customers find the best deal available. We are pleased the survey results show an increase in customer understanding and the energy industry is continuing to work with customers and consumer groups so more people understand their bills and choices.
"Already tariffs have been radically streamlined, making it much easier for customers to understand bills and compare deals. Most recent figures show that around 1.3 million customers switched in the last quarter of 2013 alone.
"This is a welcome sign we are moving in the right direction and that the process is easy to follow and the energy industry is increasingly competitive with plenty of suppliers to choose from.
"The Retail Market Review is the latest stage in improving customers' experience with their energy companies and is making the industry clearer and easier to understand. But it is also an ongoing process with more reforms still to come. As we continue to work through the reforms, constructive feedback is helpful so we can improve the information we provide."
Ofgem's consumer partner, Philip Cullum, said: "Which?'s research looks at individual elements of Ofgem's package of reforms and does not consider how all of these will work together in practice.
"In developing our reforms, we conducted many detailed research projects with consumers to understand their views of the market. We are confident that our reform package will make the market simpler, clearer and fairer for consumers and make it much easier for them to choose the right deal while still allowing suppliers to innovate in their offerings to consumers.
"The end of 2013 saw the highest switching rates ever, showing that customers are already engaging more in the market. Our new reforms are making it easier to engage by simplifying tariff choices and we have brought in new rules to ensure consumers are treated fairly by suppliers.
"Further reforms to make the market clearer, giving consumers the information they need to make easy comparisons, for example personal projections of their energy use, will come into force in April this year."
A Department of Energy and Climate Change spokeswoman said: "Last year the Government backed Ofgem's reforms to make the retail market clearer and more transparent. Simplifying the structure of energy tariffs is just one of the many reforms that are being introduced to give power back to consumers and make switching easier.
"The simplified tariffs and the new energy bills format combined with the introduction of QR codes will enable consumers to choose the cheapest tariff and have a more accurate understanding of the potential savings on offer to them.
"Someone switching from the worst deal on the market at the moment to the best online deal could save around £200 on a dual fuel bill, with 248,000 people making the switch last February and 42% moving away from the bigger energy suppliers."
:: Which? surveyed 1,515 energy bill-paying adults online in January.
Find the cheapest gas and electricity tariff for you