Art Malik is no stranger to the stage, despite being better known for his film and TV roles – which range from a psychotic terrorist in 1994 Hollywood blockbuster True Lies to a heartthrob anaesthetist in hospital drama Holby City. Over the past 30 years, the veteran British actor has worked at the Old Vic, the RSC and more recently in the Royal Court’s production of The Seagull, which played on Broadway in 2008. But in 2011, he’ll be taking on two entirely new theatrical challenges: firstly, making his Edinburgh Fringe debut, and secondly, by acting alongside a family member – his daughter, Keira.

In August, Keira and Art Malik will perform in Rose, a new play by Hywel John, in which they appear as a father and daughter trying to reconcile their Middle Eastern heritage with their life in Britain. John, a Welsh actor and playwright whose lauded drama Pieces recently transferred to New York, was last at Edinburgh in the award-winning Guardians in 2005, and Malik is effusive about his latest work.

‘It asks who is a Brit today,’ Malik tells me, ‘and what does it mean to be British. We explore the dynamic between father and daughter, which is particularly interesting here because the mother is absent. The father, who I play, calls himself Arthur because he wants to be with Britain, he wants to be more Anglicised than the English. So we explore what he desires – and what he wants for his daughter, who we see grow up on stage from the age of eight.’

At the centre of Rose is the mystery surrounding Arthur, who is hiding his past from his daughter as she tries to uncover more about her own background. But Pakistan-born Malik is insistent that he won’t bring any of his real-life relationship with his daughter into his role. ‘I think if you’re an actor, you shouldn’t need to use your memories as the key to get to your acting,’ he says, ‘Those are yours. The best thing to do is keep them to yourself.’ And although the play is billed in the Fringe programme as ‘Rose (Starring Keira and Art Malik)’, he is keen to move away from this celebrity association.

‘It’s not about Art and Keira,’ Malik explains, ‘it’s about these two characters, so I’ve been trying to keep that aside. The other day, someone asked if there were any photographs of the two of us they could use. But if I’m going to go through a family album and take out a photograph, I have to ask what the point of it is. If it’s to get publicity, then that’s not good enough. If it’s to enhance the play, then those images will be in the play. And if they’re not, then they’re staying where they are – in my private collection.’

Still, with his other daughter Jessica acting as producer on Rose and Keira having recently graduated from LAMDA, Malik is excited about a summer of working with his family before returning to his screen commitments filming the next six episodes of the BBC’s Upstairs Downstairs update. ‘I’m feeling fantastic about it,’ he says. ‘Keira is a cracking little actress. I’ve seen her do things and she’s extraordinary so I only hope I can come up to her level.’

Rose, Pleasance Courtyard, Pleasance, 0131 556 6550, 5–29 Aug (not 16), 5.25pm, £13.50–£14.50 (£12.50–£13.50). Previews 3 & 4 Aug, £6.50.