EE is still generating the most landline and broadband complaints and Vodafone is the most criticised mobile phone operator, new figures show.
However, EE has managed to reduce its volume of complaints across all services - landline, broadband and mobile - since the first quarter of this year, Ofcom said.
Ofcom fined EE £1 million in July for "serious failings" in handling customer complaints.
Vodafone continued to be the most complained about mobile provider in the latest quarterly figures, mainly driven by problems with billing, pricing and charges, complaints handling and concerns around faults, service and provision (17%).
Complaints about EE's broadband fell from 0.51 per 1,000 customers to 0.45, but not enough to shake the title of the most complained about provider.
It also continued to generate the highest volume of landline complaints as a proportion of its customer base driven by problems changing provider, concerns about faults, service and provision and complaints handling (17%).
For the first time BT is no longer the worst performer in pay TV, seeing its complaints decrease while rival TalkTalk's increased.
On average, Ofcom receives slightly fewer than 300 telecoms complaints a day from consumers.
The total volume of telecoms and pay TV complaints made to Ofcom continued to decrease from April to June, even as the number of consumers taking up these services increased.
Broadband, mobile pay-as-you-go and mobile pay monthly services saw the most notable reductions in total volume of complaints.
Ofcom's director of content and consumer group, Claudio Pollack, said: "Our complaints data allow consumers to make meaningful comparisons that can be useful when looking for a new provider.
"While it's encouraging to see a continued decrease in the total number of complaints, there is still room for improvement.
"We expect providers to make customer service and complaints handling top priorities."
An EE spokesman said: "We're working hard to improve service and apologise to any broadband customer who has not received the very best service from us.
"Last week we announced the launch of a comprehensive programme that includes a new broadband operations hub which, together with the creation of 500 new roles, is aimed at improving service levels for all of our broadband customers."