Some 92% of mobile customers, 89% of landline telephone customers and 87% of broadband customers were satisfied with their service.
But 13% of broadband customers had a reason to complain to their provider in 2016 – higher than the proportion of landline telephone customers (5%) and mobile customers (4%).
Of the broadband and mobile customers who complained to their provider in the last six months of 2016, just over half were satisfied with how their complaints were handled.
When it comes to reliability and performance, almost nine in ten broadband customers (86%) were satisfied with the reliability of their service, and 83% were satisfied with their online speeds.
Meanwhile, 86% of mobile customers were satisfied with their reception, according to th study by consumer group Which?.
It comes as telecoms watchdog Ofcom launched a new online tool enabling people to find out how well major telecoms providers serve their customers.
The online tool presents findings from Ofcom's first Comparing Service Quality report – in a simple, visual format.
The checker allow phone and broadband customers to compare how different providers rate for answering customer calls, handling complaints, and reliability of their services.
The data draws on a combination of consumer research and complaints figures, as well as statistics obtained directly from providers that have never been published before.
Ofcom chief executive Sharon White said: "We're determined to help bring about a service revolution in the telecoms sector, where consistency and excellence becomes the norm."
Ms White said Ofcom wanted to shine a light on how different providers perform, and would challenging the industry to up its game on customer service.
"We'll be monitoring closely to ensure industry service standards are raised."