Alan Yentob is having his picture taken on a staircase overlooking the vast BBC newsroom at New Broadcasting House and telling me about the flooding at his house in Somerset when we are interrupted by annoyed news staff.

They ask us to move as flashes from the camera can be seen on-screen on the BBC News Channel – illustrating the perils of having a newsroom as a backdrop for live bulletins.

Yentob apologises and we retire to his office – a former radio drama kitchen that sits between Old and New Broadcasting House. Apt, as Yentob bridges the old and new within the organisation. His office is narrow but cosy – desk stacked with books and an Alan Yentob mask someone sent him. There is a fold-up bike below his desk, just like the one Hugh Bonneville's character Ian Fletcher has as head of BBC Values in John Morton's forthcoming follow-up to Twenty Twelve, W1A, in which Yentob has a cameo.

But as there's no table, we move to director general Tony Hall's office. As he confirms, Yentob played a part in bringing Hall back to the BBC after George Entwistle resigned. "I always felt that Tony should've been the director general. Yes, I did talk to [Lord Patten] about it and I did speak to Tony. For Tony it wasn't without its risks, he loved his [Royal Opera House] job."

It seemed his influence might wane under Entwistle, but it is obvious he is now back at the heart of decision-making. As "the 'oldies', if you like", he says, "Tony and I are very close – I don't feel there's any topic we can't raise with each other" and he had a hand in assembling the new top team: "The people who have come here I've been involved with making sure they came, because I did think, where was the succession going? Now we have a number here who I think could run the BBC in the future."

Yentob has been at the BBC since 1968, been creative director for a decade and presented 22 seasons of BBC1's Imagine. Known as the BBC's "Mr Fixit", he has the experience to defend it in troubled times, such as the crisis involving the late Lord McAlpine. He admits more storms lie ahead with Dame Janet Smith's report on Jimmy Savile still to come and says the BBC must own up to mistakes such as the failed £100m Digital Media Initiative. But he argues "people need to give you credit for owning up and not simply just carry on castigating you for them", and points to the success of Freeview and the iPlayer.

Yentob is helping Hall assemble the BBC's arguments for charter renewal. One big issue is how it operates in what is "increasingly a global industry. What the BBC does for Britain and can do for Britain, if that is to be sustained it needs to be funded adequately". Netflix, Amazon, Apple, Samsung and Google, he points out, are now rivals: "These are huge players, worth hundreds of millions of dollars. They know about content, brands and acquisition and they are doing it. We are now in direct competition with these companies, [there are] very specific instances and projects where it is going on at the moment."

The BBC is a "brand that is the best of British when it's good" but it "can't compete with its hands tied behind its back and being told: 'You can't pay the talent this and you've got to disclose everything you do'. The BBC has to be as open as it can possibly be but it also has to be able to operate.

"The BBC's eye on tomorrow has been very important," Yentob believes. He is excited by technical innovations, such as iPlayer Plus and My BBC. He would like to see creative "ideas tested in a very modest way so people can feel that there are opportunities beyond just finding your way onto a main channel – places where you can try things out".

"The technology is very enabling," he enthuses, and favours handing over the cameras – to his subjects in Imagine, or to the public as BBC2's Video Diaries did when he was controller. He wants new BBC apps to play an enabling role: "Through The Space, through the BBC's Academy and through, I hope, creating some very sophisticated apps we can help others, other organisations, schoolchildren learn to tell their own stories through this technology."

Although "we've got a lot of leading women at the BBC", he admits that "we've got more of an issue on-screen and we're trying to address it. As we do off-screen with diversity in terms of leadership. On-screen we're better than we were. There's an incredible range of actors on-screen. I hope we will do the Steve McQueen project he's passionate to make. But we're not good on diversity in terms of black and Asian representation and we have to work harder."

With his often-quoted £6m pension pot and his stake in the family firm, Dewhurst Dents, why has he carried on when he might have retired?

"I love that whole egalitarian thing about the BBC. It's a bonding mechanism for Britain. It's like the NHS, it gets into trouble quite a lot and it has to explain itself and it has bits which need to be fixed."

He says the licence fee is a "glorious anomaly" and adapts a Winston Churchill quote about democracy in calling it: "the worst way of funding the BBC apart from all the other ways. That means the BBC cannot afford to be complacent about the things it doesn't get right but nor can the public or the government afford to be complacent about the BBC and score points.

"It's not just the foundations of the BBC, it's all those independent companies that [make] programmes that they care about. If you start to fragment the BBC by throwing the licence fee all over the place, you would overturn a culture, not just within the BBC, but around the creative industries which I think would be very damaging for Britain."

Does the constant press interest in his £183,000 salary and his not being on PAYE rankle? "I've been here for a long time, I've run all the channels, people have heard of me. I sound like I've got famous friends, I'm easy to take the piss out of. Every day I walk through the streets, I don't see that resentment – only from certain bits of the press, I think.

"Let's look at this double salary thing – it's not a double salary, it's half a salary. If you look at my salary for the executive role it's half what you would expect it to be. I've got a relatively thick skin. I have to put up with it. I know from my colleagues that they like working with me and there's no hierarchical feel with me."

Imagine has a loyal audience and is fed mostly by Yentob's curiosity. His friendships with artists – although criticised by some – can pay off, as with a forthcoming two-part profile of novelist Philip Roth. "Because I know him well I won't let him get away with things," says Yentob, and during it Roth says it is the last interview he is doing.

Also in the works are "quite a big ambitious thing" about being an actor, a possible film about Jerry Lee Lewis and a major project with Storyville editor Nick Fraser about social housing which "sounds boring but it's not!".

Has anyone eluded him? "The person I wish I'd met is Frank Sinatra. My daughter loves his singing, so does [his partner] Philippa. I listen to those songs and think … I know it makes me sound very old hat."