Co-operative Energy has attracted the most customer complaints ever recorded by Citizens Advice in its quarterly ranking of the best and worst suppliers.
The company, operated by Midcounties Co-operative, received 1,584 complaints per 100,000 customers - 40 times more than the best performer, SSE, figures from the consumer advisory charity show.
Co-operative upgraded its computer systems in March, with many customers complaining of being locked out of their online account or not receiving bills following the switch.
Extra Energy also performed considerably worse than in the last quarter, receiving 1,164 complaints per 100,000 customers.
Scottish Power, which ranked bottom of the table last quarter, showed signs of improvement with complaints dropping from 944 to 740.
The figures show the gap between the best and worst suppliers for handling customer complaints has increased.
The data from the 19 largest energy suppliers for July to September show SSE, EDF Energy and Green Star Energy all reduced their complaints.
Green Star Energy managed to halve its complaints ratio, Citizens Advice said.
There is little difference between the two best-performing suppliers, SSE and EDF Energy, which posted 39 and 43 complaints per 100,000 customers respectively.
Citizens Advice chief executive Gillian Guy said: "It's unacceptable that energy customers are being let down on basic services.
"Good customer service is essential to any effective industry. The fact energy consumers face such a lottery shows this market has a long way to go.
"While it's encouraging to see some companies sharpening up their act, some firms at the bottom are getting even worse.
"Pockets of improvement aren't enough. We need to see progress across the board so that every consumer can be confident of receiving a high-quality service."
Sarah Beattie-Smith, consumer policy manager for Citizens Advice Scotland, said: "We welcome improvements from those energy suppliers whose complaints have decreased, but for this to boost consumer confidence in the energy market we need a more level playing field. This will require all suppliers to work on their customer service.
"The recent spate of terrible weather has highlighted just how important it is for all households to be able to afford to keep their home warm and to be able to rely on quality service from their energy supplier."
A spokeswoman for Co-operative Energy, which has around 240,000 customers across the UK, said: "This data is from July, August and September 2015 when unexpected issues relating to the implementation of our new IT system were at their peak. Since then, we have fully resolved 93% of complaints that were referred to the Ombudsman and are working through any remaining issues.
"The level of service our customers now receive has significantly improved. Call response times have halved over the past six weeks and we have recruited and trained over 100 new customer service staff. We are making further improvements to ensure our customers receive the high level of service they expect and deserve."
Extra Energy managing director of operations Ben Jones said: "We are extremely sorry for the issues some of our customers have experienced between July and September this year. We've grown very quickly, and as we've grown we haven't been able to put in place sufficient customer services resource - largely because of limited capacity at our former offices.
"We have now moved to larger offices, which has helped significantly improve our service levels over the past month. We have also hired more than 100 extra customer service staff and extended our call centre opening hours by an extra four hours every day.
"Call waiting times have reduced by more than 90%. We appreciate the affected customers bearing with us while we work to provide them with the quality service that they rightly expect."