The firm received 34 complaints per 100,000 broadband customers between January and March, ahead of TalkTalk on 29, Plusnet on 25 and EE with 24.
It also had 19 complaints per 100,000 pay TV customers - significantly more than second worst Virgin Media (nine) and best performer Sky on two.
TalkTalk topped the table for landline complaints with 22 per 100,000 customers, closely followed by Plusnet and Post Office, both with 21, BT (20) and EE (19).
Vodafone was the most complained-about mobile provider with 17 complaints per 100,000, significantly more than TalkTalk and Virgin Mobile, both on eight.
Ofcom said complaints about landline services increased on the previous quarter, while pay-monthly mobile complaints fell and broadband and pay TV complaints remained stable.
The regulator publishes the figures to help consumers compare performance when choosing a supplier, incentivise companies to improve customer service and address recurring problems.
Lindsey Fussell, Ofcom's consumer group director, said: "Our report shows that, for a number of providers, there is still much room for improvement.
"Phone and broadband companies must take all possible steps to improve their complaints handling and customer service, and we expect this to be their number one priority."
BT said: "We apologise to customers we've let down. BT cares about the service it gives and we're investing heavily to make improvements.
"Customers are seeing an improvement as these initiatives take effect and we now publish key service statistics quarterly to be transparent about our progress.
"Although Ofcom received more complaints about BT, we note that Ofcom state this data provides only one lens on performance and that their own research published in April indicates that other providers' customers may have had more reason to complain than BT's and in many cases other providers are less effective at resolving complaints."