He also denied suggestions that Ofcom does not trust BT to run its Openreach business.
The telecoms watchdog is to take formal proceedings with the European Commission to force BT to legally separate its Openreach network arm after it said plans to appease competition concerns fell short.
Openreach develops and maintains the UK’s main telecoms network used by telephone and broadband providers, such as Sky, TalkTalk, Vodafone and BT Consumer.
Ofcom believes a more independent Openreach is important to improving services across the UK.
Sir Michael told ITV’s Peston on Sunday: “Everyone is frustrated because they want superfast broadband today because it’s a utility... we’re committing to delivering.
“Just to point out that Ofcom and the OECD (Organisation for Economic Co-operation and Development) and every independent survey showed this is one of the fastest roll-outs of broadband ever in an OECD country with some of the lowest speeds, most competition and highest access.
“The point that I think is something that we have to work on is customer service has not in the industry as a whole been good enough and we’re doing a lot to improve that.”