So what did the manic and acclaimed tenth Doctor do next? After leaving Doctor Who in 2010 after four years in the high-profile role, there was a brilliant, sell-out Hamlet on the London stage, radio plays, audiobook readings, voice-overs, a surprisingly dud film, an unsuccessful attempt at an American TV series, and the voice of Charles Darwin in the Aardman animation The Pirates! In an Adventure with Scientists. "I'm ridiculously proud of that. It was a real treat," says David Tennant.
He's chipper, grinning, boyishly enthusiastic as ever, even though he's 41. If he weren't so tall, elegant, slim, and fashionably unshaven, he'd resemble a goblin, with his bright, expressive eyes that sometimes seem a little overwhelming on screen. "Do they?" he asks. "Well, you can only work with what you have."
He takes success and failure in his stride and explains, over a glass of tap water, that his career is a battle for challenges. He's just finished filming the lead in The Spies of Warsaw for BBC4, adapted by Dick Clement and Ian La Frenais, and is due to film a new ITV1 drama series called Broadchurch.
"I'm always looking for a new project. There's a kind of exhaustive adrenaline push, which is alarming and overwhelming, but very motivating. It's fear of failure: is this the one where they discover I don't deserve to be at the party? I wait for someone to say, 'You've had a good run. Now it's time to go.' I admire other actors' work and then see mine and it seems false and crass. As an actor you put yourself up for appraisal on a regular basis and ask for your insecurities to be tweaked. No wonder I'm a nervous wreck," he laughs.
In fact few actors seem less neurotic. He's famously discreet - married on New Year's Eve to an actress, Georgia Moffett, 27, who he met on Doctor Who in 2008. They have a daughter, Olive, born in March last year, and he's adopted her ten-year-old son Tyson. He's had one or two skirmishes with the press: "I've had a go at them. I'm not suggesting my phone was hacked, although it would make sense of certain moments in my life when I was surprised about how some information became public.
"It's difficult to do anything about inaccuracy or intrusion even if you think you have a good case. It becomes very expensive, very quickly. Grapple with the Daily Mail and you're up against some serious lawyers. They have a weird power. Perhaps actors should keep quiet. The brutality of the learning curve when you start doing interviews is quite steep. Things you say can go very badly awry, so you end up being protective and too circumspect, which is a shame and makes everyone's job harder."
"At the same time, you understand what you're getting into by being on TV. I'm not that naive. But there's a sense that everyone in the public eye has to have moral purity. Personally I might agree that's a good thing but I don't see why, because you're in a TV programme, you have to be perfect. Actors often get a bad press, but 87.5 per cent are down to earth and reasonable. Difficult ones are becoming rare because the world doesn't allow it. They're usually not the big stars but those who believe they should be."
Perhaps emotions are best dealt with in fiction. This week he stars in the first of five half-hour stories under the title, True Love. Written and directed by Bafta award-winning writer and director Dominic Savage, they explore, in improvised dialogue, various aspects of love. Subsequent episodes star Tennant's former Doctor Who co-star Billie Piper, Jane Horrocks, Ashley Walters and David Morrissey.
It's set in Margate, where Savage grew up. "Doesn't the town look beautiful," says Tennant. "There's something inherently romantic about the seaside, and because Margate is small it allows characters to interweave and return in future episodes."
In the film he plays Nick, a loving husband and father unexpectedly confronted by the first love of his life. The evening before we meet he'd watched the finished work for the first time. "I was taken aback. It wasn't what I expected. We were given a storyline, but no dialogue, which I've never done before. It was made up on the spot, which was difficult. I should be paid as a writer," he jokes.
"But Dominic made it OK for us to go wrong. At the risk of using a pretentious-sounding word, it was 'organic'. He'd give us a paragraph of what might happen in a particular scene - 'Nick talks about his family', for instance - but it was still terrifying. At first you talk all the time, trying to fill the silence. Dominic told us it was fine to say nothing. And there are a lot of pauses, which work well because so much happens. Huge relationship moments are unpicked. You look for a hook from your own experience, which allows you to be truthful, because this is about recognisable emotional lives we can all key into."
So has he ever been contacted by a former lover? "Mmm. Well, yes, but I've never been in Nick's situation where there's suddenly an alarming set of circumstances. And it's very raw. Dominic has found a way to show how emotional relationships are delicate, complicated and multi-faceted, which you don't often get in TV drama. There's no suggestion that Nick isn't deeply in love with his wife, but he has this moment… there's nothing morally robust in the way he copes. It's messy and the drama is non-judgmental, which is important. It's too easy to condemn behaviour. We're all struggling with stuff… all the time."
Could he imagine himself being unfaithful in a similar situation? He smiles. "Of course not. The Daily Mail would have my guts for garters. And they'd have pictures."
He was brought up with a brother and sister near Paisley, where his father was a minister and at one point Moderator of the General Assembly of the Church of Scotland. "He talks about wanting to be an actor when he was younger, but growing up in Scotland at that time it didn't seem a possibility. Then he discovered a vocation, which he's thrived on. There's a great deal of performance being in the pulpit and he does it with brio and panache. He did appear in Doctor Who [as a footman, a non-speaking part] and that was great fun."
"I was lucky because I knew what I wanted to do from the age of three - although that seems unlikely and when I look at three-year-olds now it boggles the mind. I find it remarkable that nothing happened to steer me into a more explicable career. It must be luck as much as circumstance.
Although he's had few bleak professional periods, Doctor Who was a career changer. "I'm very glad it happened. Mercifully, I haven't been type-cast and it opened more doors than it closed. I was never bored, but I wanted to make sure I left before it became a job. It's still thriving and Matt Smith is brilliant in the part."
"Of course I lost a certain amount of right to privacy, which is not what I'd choose, but I accept. No one can teach you what it's like to be observed in public. I remember, before I was that person, watching well-known people walk into a room - you imbue them with inner confidence and a slightly royal presence. Yet when it's you, it's terrifying. People lean over in restaurants and say, 'Don't look now, but that's him off the telly.' Very peculiar. I'm not moaning - there's nothing worse than that, because there are huge advantages - but you feel vulnerable. The world's perception of you has changed while you remain the same."
Expectations increase, too, so it's difficult when they're not fulfilled. He went to Los Angeles in 2009 to make a pilot for a legal drama series, Rex Is Not Your Lawyer, in which he played a brilliant litigator who suffers panic attacks. "I thought, 'Why not?' and it was a wonderful experience even though it didn't limp to a series. I'd feel better equipped if I tried again."
Two films were not a huge success. In Fright Night (showing on Friday at 10pm on Sky Premiere), a remake of a 1985 vampire film, he played a leather-trousered Las Vegas showman and vampire hunter. "It was well received critically, but no one went to see it." Earlier this year The Decoy Bride was released to almost universal scorn, even though he seems the ideal choice for such a romcom, in which a famous American actress (Alice Eve) tries to avoid unscrupulous media attention ruining her wedding to an author (Tennant) by holding it on a remote Hebridean island. The problem is it's a cliché-fest with ludicrous dialogue.
"Has it been slammed?" he asks. I tell him, "big-screen dross" is a typical comment. "That's not nice. It's disappointing when something in which you've invested time and love isn't well received. But there's little you can do. As the years trundle on you become objective. I thought it was a lovely film, but critics probably aren't writing for its intended audience."
"Doing something new is the point," he repeats. Every fresh project is a gamble. You draw a deep breath, and ask yourself, 'What's the worst that can happen?' and the answer is, 'That it's not very good?' You can't worry. You do your best, and think, 'This works for me, at this moment, for whatever reason.' I just hope I get another job at the end of it." There s no danger of that not happening.
WHO ARE THE STARS OF TRUE LOVE?
David Tennant (Nick): When happily married Nick is reunited with his first love, his emotional world is thrown into turmoil.
Billie Piper (Holly): Unhappy in her relationship with a married man, teacher Holly is drawn to someone new - one of her female pupils.
David Morrissey (Adrian): Divorcee Adrian is determined to find true love but the spectre of obsession threatens his faith in romance.
Jane Horrocks (Sandra): Now her children have gone, will empty-nester Sandra stay with her husband or embark on a new life with her soulmate?
Ashley Walters (Paul): Feeling pushed out by the birth of his son, young dad Paul is torn between desire and dreary domesticity.