A former BBC boss has called on Rishi Sunak to say “something interesting” about how to change the rules over appointing the new chair of the corporation.

Lord Tony Hall, who was director-general of the BBC until Tim Davie took over in 2020, said the Prime Minister “ought to” give up the power to choose who should take on the role following the resignation of Richard Sharp.

Speaking at the Voice of the Listener & Viewer (VLV) spring conference on Thursday, he said: “The BBC is a broadcaster that is paid for by everybody and it should be independent, and its independence is fundamental and I think anything which helps to reinforce that is really important.

“When you then say, well, the Prime Minister appoints the chair, then there’s a sort of wry grin and, you know, people think, well, is that really the independence that you keep talking about?”

He said he “probably” could not see the process not changing before adding: “I think (Sir) Keir Starmer’s said interesting things on that.

“I think (it) would be very good if the current prime minister said something interesting about that as well but probably the right time to do that is wait until it comes up to the charter renewal in 2027.

“I think the more you can do to show that the board of the BBC is independent, the better.”

It comes after Labour leader Sir Keir said his party would replace the Government’s power to appoint the chair with an independent process.

Mr Sharp stepped down after he was found to have broken the rules by failing to disclose he played a part in getting Boris Johnson an £800,000 loan guarantee.

Earlier in the week, Culture Secretary Lucy Frazer said she is looking “very closely” at the BBC licence fee, as she dismissed calls to remove political interference from the appointment of its chair.

She also said Mr Sunak will appoint the “best candidate” to replace Mr Sharp as BBC chair, regardless of their political ties.

Lord Hall, who sits on the House of Lords communications and digital committee, also advocated for more transparency on who is being appointed to the panel that recommends the BBC chair as well action on the licence fee.

He also said he had been “pushing like mad” for a household tax instead of a licence for paying for the BBC and now wants a progressive system.

Lord Hall added: “So I think that the challenge … between now and 2027 is to find a fair way of paying council tax or licence fee and boringly I would go for licence fee, but with some sort of gradation because I think there are people who would actually pay more. I mean, you know, I would for one.”

He was also asked about whether there should be a gathering of a cross-section of society, called a citizens’ assembly, to look at the future of the BBC.

Lord Hall said: “I don’t know who should fund that but exactly (that) sort of thing … would be really, really helpful.

“I mean, it seems to me look to Ireland and (you) see some very big controversial issues have been sorted out using citizens’ assembly, as I understand.

“So I think applying that to the BBC would be really useful and could surprise everybody.”