Boxing’s like acting; to improve you’ve got to be in classy company.”The danger of that tactic is that you can quickly look outclassed, out of your depth Which might well happen to Harrison. But to Winstone? Not a chance.’Lenny Blue’ is on ITV 1 next Monday and Tuesday at 9pm. The image of Josie Lawrence that is lodged in my head, and I suppose in lots of other people’s, is Josie the Improv Queen on Whose Line is it Anyway? – bright-eyed and bushy-tailed, flying by the seat of her pants as she cheerily belted out impromptu lyrics with atrocious rhymes at top speed: a mercurial, spontaneous talent. But that was a while ago; these days, her career revolves around careful preparation and repetition. Now she is appearing in Bryony Lavery’s three-hander Frozen at the National Theatre – a transfer of the premiere production, which was staged at Birmingham Rep in 1998. You can’t get much less spontaneous than that.The reasons for this long-delayed transfer aren’t entirely clear. Lawrence says that there was talk of moving to the National back then, when the play had received some rapturous reviews, but no stage was available.

Four years on, out of the blue, the call came saying, How about now? She says she didn’t even have to think about it: so now she is reunited with the original cast, Tom Georgeson and Anita Dobson, and the director, Bill Alexander.It is a sombre play. Georgeson plays a serial killer who specialises in young girls; Dobson is the mother of one of his victims. Lawrence plays Dr Agnetha Gudmundsdottir, a criminal psychologist from New York, visiting Britain to pursue the question “Serial Killing – a Forgivable Act?” The play includes extended monologues as well as dialogue; and Lawrence’s part includes an academic lecture.For Lawrence, this second bite at the cherry is a very happy experience. One reason, she is evidently consumed with awe and affection for her fellow actors, and for Bill Alexander – he also directed her in a 1996 production of The Alchemist.

But another reason is that, despite her background in improvisation, she evidently gets a kick out of doing a part over and over again. As she tells it, this is not a rejection of her roots in improvisation so much as an extension of it: “When I did Mrs Anna, people said ‘How could you do something for that long?’ … But I have always been someone who enjoys going on stage and finding new things out every night. I don’t want to sound too actory, but I like keeping things fresh.”She recalls the pleasure of constant rediscovery during a run of The Cherry Orchard at the RSC, in which she played the servant Dunyasha: “The very last night,” she says, “I found out something I’d never found out about her.” On enquiry, this turns out to be a very trivial matter: she had to drop some teacups, breaking a saucer, then clear up the mess with her hands; she kept cutting her fingers on the shards.

What she realised on that last night was that she could scoop the shards into her apron – this was not only kinder on her hands, but also looked rather good.From that, you might judge that she is one of those actors who finds the character through external details, rather than using the details to express a preconceived idea of the character – the very opposite of Method. You might also think that she is not inclined to intellectualise the processes of acting. When I ask her what it was like to pick up Frozen four years after she left off, she says “Well, that was very interesting,” but follows up with generalities about “finding stuff we’d missed the first time round, just little details that you could tweak because you were aware of the shape of the play”, and seems a little uncomfortable with the idea of going into more detail. But she is also simply grateful to have been chosen for a serious part, since she does not see herself as obvious casting.”I know that Whose Line Is It Anyway? made me a kind of household name for a while, and that was great, and I’m completely beholden to it – I think for a while I used to try and back off away from it, ‘I do more than that, you know’.” These days, she’s quite happy to be recognised because of the programme; but, she says, “There have been occasions when I haven’t been able to audition, even, for a part, because the powers that be on that particular project have said ‘She’s a comic’.”If that’s so, it’s very shortsighted. My abiding memory of her on stage comes from Gale Edwards’ production of The Taming of the Shrew for the RSC in 1996, in which Lawrence played Katherine. Her final speech of perfect wifely submission, more than problematic for modern audiences, is sometimes treated ironically, with a nod and a wink to show some complicity between Kate and Petruchio.