Your new sitcom is called Family Tree. Do you have an interest in genealogy?

The sitcom began when I was going through the things my father left when he died. There were boxes full of photographs, diaries, toy soldiers, his war medals… I began to research my family tree, which has branches going back 800 years, and this struck me as being an interesting starting point for a story. It became a show about the lead character Tom [played by Chris O'Dowd] searching for his ancestors.

The show feels very British. Do you feel that way?

Oh yes. I have dual citizenship. My dad [diplomat Peter Haden-Guest] was born in London and I lived there a lot as a child. Britain's like home. I have such history there. When my dad died, he was sitting in the House of Lords. I was in London editing a film and ended up sitting in the Lords too. It was everything you'd imagine. Very interesting.

You don't audition actors, do you? You just chat…

[Chuckles] Yeah, we "chat". It's an Official Chat. It's difficult to articulate how I know it's the right actor but I do. It's instinct. Intuition. And then we all just jump in. My daughter recommended Chris O'Dowd to me after seeing him in Bridesmaids, so I watched that and his sitcom, The IT Crowd. When I was over in London we met up and I knew immediately he was the right person. The interesting thing about Chris is that he can be the funny guy and the straight man at the same time. That's quite remarkable.

You're famous for your improvisational way of shooting. How does that work in practice?

We do detailed character histories and all the scenes are delineated, so it's not just a random thing where they're yapping away. I meet with the actors and discuss the scene, the relationships. Then we go on the set and shoot. There's no rehearsal because that would kill the spontaneity. On average we only do two takes. It's a very different method to anyone else's that I know of.

There's a ventriloquist character in the show [played by Nina Conti], and you played a ventriloquist in your 2000 film Best in Show. Is it an interest of yours?

Strangely enough, among my dad's things I found the diary of an ancestor who was born in 1797 and became a ventriloquist in London. That was quite chilling. It described exactly how I was as a child but 150 years earlier – doing voices, pretending to be a ventriloquist.

Michael McKean, aka David St Hubbins from This Is Spinal Tap, gets to do his English accent again in Family Tree. Was he rusty?

It took him a little time to roll back into it. Michael's an incredibly gifted improviser but he doesn't know anything about football, so I had to explain the sport to him because his character's a big Tottenham fan.

Do you know your football?

I do. I've been following and playing it since school. I watch maybe three matches a week. Am I a Spurs fan too? No. I do have a team but we'll leave that for another discussion [laughs].

You normally make feature-length films, so how did you adjust to a half-hour sitcom?

Family Tree lent itself to this format because it doesn't really have an end – Tom can just go on tracking down his family in far-flung places. But it had to be a TV show without commercial breaks, because I don't know how to write tiny segments. It had to be on a network that allowed us to make small movies, which is how I look at this. They're eight little films. The editing process was very different. Normally I take 18 months to edit my films, but this had to be done concurrently as we were shooting. I had two editors and we were editing over the internet in my hotel room after the day's shooting, which was… interesting. A challenge.

Ricky Gervais freely admits he ripped off the mockumentary style you popularised with This Is Spinal Tap. Are you a fan of his?

The Office is an amazing show. So is Extras. I'm a good friend of Ricky's and think he did a brilliant job.

Do you see the similarities?

There's a vague similarity, but his shows are scripted and mine aren't.

The Stones headlined Glastonbury last month but Spinal Tap beat them to it…

That's true, we played the Pyramid Stage in 2009. It was a fantastic show. There were 130,000 people there or something. Since the film 30 years ago we've gone on tour, playing Wembley, the Albert Hall, Carnegie Hall… It's weird but great. The fiction became real.

Any chance of a Tap reunion soon?

We get asked to do shows on a regular basis. But what I will say is that we're in the midst of talking about something for next year…

Family Tree is on Tuesdays at 10pm on BBC2