The report, covering the last three months of 2013, was published by Ofcom.
The communications watchdog ranks the five biggest internet providers based on the number of complaints it receives about them adjusted according to the number of customers.
It marks the first time EE has not led the name-and-shame list in over a year.
Virgin Media had the lowest level of complaints, followed by Sky for the fourth quarter running. TalkTalk came third.
According to the figures, Ofcom received 32 complaints for every 100,000 BT fixed-broadband customers between October and December last year. They related to service faults and the way BT's staff had initially attempted to handle the reported problems.
The firm was also found to have generated the highest level of complaints about its subscription TV service: 31 per 100,000 customers. The category covers access to the facility and billing, but not the quality of its programmes.
"BT is disappointed with the results in broadband and TV, despite the fact that we've improved from last quarter," responded Libby Barr, managing director of BT customer service.Virgin held on to the crown for having the lowest level of complaints passed on to Ofcom
"BT is the fastest-growing business by far in the UK for both pay TV and broadband, and as we process more transactions we have unfortunately suffered more disruption than companies with static or declining customer bases."
In response to this claim, Virgin Media noted that it had increased both the number of its broadband and pay-TV customers over 2013.'Improving sector'
The level of complaints about EE's broadband reported by the regulator was nearly 60% lower than for the same period a year earlier. But the firm said it still had room to improve after Ofcom reported receiving 29 complaints for every 100,000 subscribers over 2013's final quarter.
"We are of course disappointed by these latest results and will take on board the findings of the Ofcom report. We have an ongoing programme to improve service performance," said a spokeswoman.
Andrew Ferguson, editor of the Thinkbroadband news site, told the BBC there was plenty to be positive about.
"The general trend over time is that the average number of complaints is down, so broadband does seem to be a sector that is improving," he said.
"It may be a factor that people have become better at understanding the problems you can have with it and also the various regulations that have come out of Ofcom.
"For example, firms must now let customers walk away if they change prices."