David Tennant felt "huge responsibility" starring in new BBC comedy There She Goes

“No, not me,” the 47-year-old insists, when we discuss the BBC4 series. “If anyone’s been brave it’s Shaun in writing it. He’s so honest about his journey with his daughter, how he’s come to terms with that, and his very understandable shortcomings.”

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A couple having a daughter with a disability is not natural comedy material – Tennant’s co-star Jessica Hynes calls it a series about “parents going through dark nights” – but Tennant says he wanted to do it from the moment he read the script.

“The writing was so real, so touching and so unexpected,” he says of the screenplay by Pye, whose daughter was born with a rare chromosomal disease in 2006. “It was unlike anything I’d read before. It’s such raw, human stuff, I felt a huge responsibility, especially with Shaun in the room when we did the read-through.”

If that sounds a little heavy, then Pye points out, “The central message is that although getting this news about your daughter is on that list of things you never want to hear in your entire life, for this particular family, it’s going to be all right.”

Tennant and Hynes play parents Simon and Emily, and the series unfolds over two timelines: in 2006, as the couple respond to the news that their unborn daughter has a potential brain abnormality; and in 2015, when that daughter, Rosie, is nine.

Rosie is played by Miley Locke, who has previously starred in The Royals and Grantchester. She doesn’t have a disability, but Tennant says: “I think children can rather innocently and beautifully portray that without it being self-conscious. Miley really captured the essence of Rosie in a very true and very real sense. Which was something really quite remarkable to witness and not easy to do.”

Rosie’s disability disrupts family life profoundly; she is given to throwing herself to the ground and going ominously stiff. Pye, who has written for Would I Lie to You? and Never Mind the Buzzcocks, finds humour not so much in Rosie’s condition and quirks but in the way Simon falls short of the parenting mark. He is inclined to avoid his responsibilities, reaches for the bottle when under stress and sulks when he doesn’t get his own way. Emily tends to soldier on. It works partly because there is such a strong rapport between Tennant and Hynes, who worked together on Doctor Who in 2007. “I know David so well,” Hynes says. “That makes it very easy for us to slip into the back-and-forth that Shaun sets up between us.”

Tennant, who is married to the actor Georgia Moffett, says the series has affected the way he feels about fatherhood. “I defy anyone with children not to see moments of what it’s like to be a parent within the series. It makes you wonder how you’d react in that particular set of circumstances, of course, but it also makes you wonder about the ways you might have reacted in your own life as a parent, about the times you got it wrong and the times you got it right.”

The couple have three children, Olive, Wilfred and Doris, and Tennant adopted Tyler, Moffett’s son from a previous relationship. “It’s only since I’ve become a parent that I’ve thought, ‘Why are there not more dramas about just being a parent?’” Tennant says. “The ups and downs, the contradictions… that sense of being sent home from a hospital with a child that you’re then expected to know what to do with.”

Tennant met Moffett on the set of Doctor Who in 2008. Moffett – who, to confuse things, is the real-life daughter of Doctor number five, Peter Davison – played Tennant’s daughter Jenny. It’s just one way in which Doctor Who is woven into Tennant’s life. When Jodie Whittaker was announced as the new Doctor, Tennant, who starred alongside her in Broadchurch, told her, “This is one of the most amazing things that can happen to you. There are only a few of us who know how it feels.”

Whittaker says her response to this advice was, “Oh, wow! Cool, cool, cool, cool, cool,” but Tennant doesn’t sound like a man with a strong emotional attachment to a series that took him from playing Casanova to national stardom. “I’ve got nothing to do with the show now,” he says. “Obviously, I’m aware of it, like everyone else in the country, but I don’t feel any...” and then he stops and, unusually for an actor in mid-interview, changes his mind.

“No, that’s not true, I do feel a personal connection to Doctor Who. It’s just that I’m not living it every day like all the people who have been ramping up for the big launch right now. For them, I’m sure it must be slightly overwhelming right now as the series begins.”

I’m curious about what order of precedence he gives his past successes, from playing the Doctor to his 2009 screen Hamlet and, from 2013 until last year, DI Alec Hardy in Broadchurch. “You want me to list my past successes!” He scoffs. “I think I’m far too much of a Scottish Presbyterian to think of myself like that.” Tennant was born in West Lothian, the son of a Church of Scotland minister, with Ulster Orangemen ancestry. He stars alongside Saoirse Ronan in Josie Rourke’s upcoming Mary Queen of Scots – Tennant plays the ultimate Presbyterian, John Knox, the Scottish cleric who started the Reformation north of the border and supported the execution of the Catholic Mary, Queen of Scots.

“I think there’s a definite west-of-Scotland upbringing that I had and I think many people of my generation and social circumstances will recognise,” Tennant says. “There’s often the sense of ‘who do you think you are-ness’ that I find useful. It’s grounding and a good reminder sometimes that you’re not as fancy as you like to think you are. I think I cherish that part of my upbringing, and I certainly can’t shake it off.”

It also, perhaps, makes a pretty good mask to hide your feelings behind when you’re waiting for the birth of a child. “Yes, that’s a very vivid concern,” Tennant says. “The fear that you won’t be able to cope if your child is anything less than ‘perfect’. But Shaun and his family now have a life that they cherish. And Shaun’s journey, and his wife’s journey, from fearing that they wouldn’t know how to love this daughter, to actually being passionately in love with this little girl and finding an unexpected life, in an unexpected direction – I think we can all identify with the humanity of that.”

It’s rare that an actor has a genuinely profound experience when he’s making a comedy. Will it make him a better dad? “I think it’s hard to know,” he says. “It’s one of the constant questions about acting, or when you spend a bit of time in someone else’s shoes. Does it rub off on you, does it make you a different human being? We evolve as parents, as our own children grow older, and as we experience and witness other people’s families. I hugely admire and respect Shaun and his family. And as a parent I can only aspire to that.”

There She Goes first airs on Tuesday 16th October at 10.00pm on BBC4