Ten people who changed the world: Sofie Grabol, star of The Killing

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That was a short but sweet cameo by actress Sofie Grabol in Absolutely Fabulous on Christmas Day. You surely saw it. Eddy Monsoon (Jennifer Saunders) fell asleep while watching The Killing on her laptop and dreamt that Grabol's character Sarah Lund, dressed in trademark jeans and Faroese sweater, was nosing around her bedroom in the manner so beloved by fans of the BBC4 drama, lifting and inspecting objects and her searchlight gaze sweeping the room as Eddy gabbled in made-up Danish.

What I really like is when Lund turns that laser stare on suspects, the eyeballing intensifying into what could be mistaken for amusement, a half-smile lighting up her eyes when the interviewees begin to leak clues. I started thinking of it as The Look. This penetrating, half-obsessed woman really was the television character of 2011 (hence her elevation to Ab Fab cult object) – or 2007, since that was when Danish Broadcasting Corporation made the 20-part thriller. We've since had the 2009 follow-up series, the 10-part The Killing II, but it didn't quite have the same impact. How could it?

So, Lund. Or can we call you Sarah? First, let's get the woolly jumper thing out of the way because that became a little bit less funny every time someone mentioned it. I was more intrigued by the handbag – an unremarkable, brown leather satchel-like thing that did more to establish Lund as average working woman than any old sweater or worn-out jeans or messy private life. Oh, and that private life.

Bengt, the long-suffering boyfriend trying to lure his Sarah to a new life in Sweden, Lund's mother, desperate for her daughter to start that new life, and Lund's teenage son (not so keen on Sweden) – they were always last in the queue when police matters called. Grabol understood the need for Lund to remain apart. She was also vigilant about being thrown into opportunistic romantic sub-plots, as when the writers decided that Lund should have an affair with the Copenhagen politician Troels Hartmann. The actress rushed into the writers' office and accused them of selling out, recalling saying: "I am Clint Eastwood! He doesn't have a girlfriend!". And what about the scene in The Killing II where she nearly kisses...? Never mind who she nearly kisses, because I know that many readers have recorded the series to watch later.

And that is the key to Gabrol's Lund. She is Clint, yes, and she is the classic Chandler-esque loner, for down these mean streets a woman must go who is not herself mean. I met Grabol a couple of months ago and she didn't disappoint. More glamorously dressed than her character (how could she not be?), Grabol struck me as a proper actress with a hard-won integrity, and what impressed me more than anything was her revelation that she nearly didn't sign up to the second series. Leave them wanting more – it's why she changed her sweater for The Killing II.

A star in Denmark for the past 25 years, and moving freely between the stage and television work – from Shakespeare and Strindberg to shows like the Emmy-winning Nikolaj og Julie (a sort of Danish Cold Feet) – Grabol was hitherto best known for her more emotional, tearily-traditional female roles. For viewers in her native country to see Grabol as Lund must be like British viewers suddenly confronted by, say, Juliet Stevenson playing James Bond.

That masculine stance was Grabol's way into the character – she copied her (male) director's manner of walking, standing and sitting – and you can see it best when Lund perches on the edge of a table, legs casually apart. Lund also has a very masculine monomania, what her exasperated superiors call "tunnel vision", a ferocious concentration on the case at hand to the detriment of everything else.

Is she a feminist role model? More post-feminist, really, and interestingly Gabrol compared The Killing directly to the Prime Suspect series, in which Helen Mirren as DCI Jane Tennison was defined by the antagonism of her male colleagues. A decision was made with the Danish series not to make Lund's sex an issue. And refreshingly she is given the minimum amount of back story – back stories being the bane of modern TV drama. The Killing III, for example, has just finished filming in Copenhagen and Grabol told me that everyone concerned faced a dilemma with the new series because the detective gets her own flat. How to decorate and furnish it without revealing too much of Lund's personality? This is a woman, you feel, who would happily live in a bare room, with just a bed and a chair on which to hang her handbag. Oh, and OK, also the sweater. For just as The Killing has revolutionised what can be done with that most hackneyed of all genres, the whodunit, so Sarah Lund has redefined the female police detective – indeed female protagonists generally. "Skol!" as they say in Denmark.