The BBC invited audience members to have their say in a series of on-air promotions across TV and radio. It also sent emails to 40 million BBC account holders.
The results of the Our BBC, Our Future questionnaire come after the relationship between the BBC and the government has been in the spotlight.
Culture Secretary Lisa Nandy appeared to call for Mr Davie’s resignation this summer after a string of scandals, including antisemitic comments by punk duo Bob Vylan at Glastonbury being broadcast on iPlayer, and the revelation that a Gaza documentary was narrated by the son of a Hamas official.
In August, former BBC director of news James Harding told the Edinburgh TV Festival that Nandy’s involvement in the Bob Vylan scandal was “chilling”, and criticised “political interference”, or the perception of it, at the BBC.
Last year, BBC chair Samir Shah said there was “an almost perpetual government review over the BBC” as a result of the requirement for ministers to renew the broadcaster’s royal charter every 10 years.
Meanwhile, questions about the BBC’s independence were raised when former Tory donor and Rishi Sunak’s ex-boss Richard Sharp was named BBC chair in 2021. Mr Sharp resigned two years later over his links to Boris Johnson.
Also in 2021, Theresa May’s former communications chief Sir Robbie Gibb was appointed to the BBC board.