“We expect providers to make customer service and complaints handling top priorities," said Ofcom's consumer group director Lindsey Fussell.
"While complaints have gone down, providers must work harder to better serve their customers.
"Consumers have a right to expect good service and will rightfully complain when that standard isn't met. If companies do fall short, we will step in and investigate, which can lead to significant fines."
Following the trend from the previous three month period, Sky fared pretty well, picking up the fewest complaints for its broadband, landline and pay TV offerings.
And Vodafone remains the most complained about mobile provider, a position it also occupied this time last year.
The total volume of telecoms and pay TV complaints made to Ofcom reduced between the first quarter of 2016 and the second quarter, the watchdog said, with declines in landline, broadband and pay-monthly mobile complaints.
BT was the most-complained about broadband firm, with 26 complaints per 100,000, followed by Plusnet, with 23.
TalkTalk was the worst performer among landline providers.
Vodafone was by far the most complained about mobile phone operator, with 23 complaints per 100,000. TalkTalk was next, with eight.
Meanwhile, Sky garnered the fewest complaints among pay TV providers.