Mr Davie said: “The vast majority of households think it offers very good value. That’s what the BBC needs to focus on. Under my leadership, we’ll focus on that.”
He told a virtual conference of regulator Ofcom that the broadcaster has more work to do to connect with all viewers.
He said many aspects needed “modernising” to reflect the whole of the country. Mr Davie said tackling “socio-economic diversity, different types of people, different voices” was a problem “as big as anything”.
He added: “What is Britain? It can’t be that we’re just taking people from a certain academic track.
“We’ve got to have a broader sense of what intelligent reporting is.”
He said trust in the BBC had grown over the past year: “But I get a sense in our research that there are certain people who do not connect with us… that’s about out of London, it’s about programming choices, who speaks for us, who we put up in the newsroom.
“All those things need modernising to represent what is a more diverse Britain.”
He said he was “not just talking about traditional” concepts of diversity. “I’m talking about how secure you feel in your life, how comfortable you feel in your community, all of that.
“We need more diverse voices and that is a challenge for every single institution, not just broadcasting.
“l have lit a fire on this. We won’t recruit in the same way and we need to look more broadly across the UK so that everyone says ‘the BBC is for me’ and ‘my views are represented’.”
Asked about an increase in non-payment of the licence fee, Mr Davie said it “is marginally up…we’ve got 25 million paying households”.
He added that “in a more competitive environment you’re going to get some erosion” but “we are in a good position”.
Mr Davie said the pandemic had seen a rise in the numbers of people who said they value the BBC.