One reason why the real Churchill is a guarded secret is that she fights so shy of media attention. She's wary of giving interviews and when you do get to talk to her you're rarely allowed to stray into personal questions and gossip. (It's only because she asks about my own children that I discover she's already a grandmother.)
But the other reason is that her plays differ so radically from each other. You can't deduce from them a specific Churchill territory, a specific Churchill stance. Certainly her latest work is a far cry from the city slick of Serious Money - The Skriker is a piece peopled by characters from fairy tale and folklore, where the text is fleshed out by sections of entirely independent music and choreography.
The obvious question is why this vertiginously articulate writer should turn to the most non-verbal of art forms, dance; why she should want to fill a play with movement when she's so adept at spinning words. In fact, Churchill isn't a stranger to dance. In 1986, with the director Les Waters and the choreographer Ian Spink, she collaborated on A Mouthful of Birds for Joint Stock Theatre Company, integrating the text with a sophisticated language of movement and gesture. Since then she's also worked with Spink on two other projects where text and dance pushed each other into new dimensions.
Fugue (1988) was a formal dance of words, images and movement made specially for television. Its rhythmic, fragmented text and surreal cutting between fantasy and reality made Dennis Potter's films look straightforward. Lives of the Great Poisoners (1991) was a kind of dance opera, with music by Orlando Gough, a cast of talking dancers, and singers who moved in choreographed groups.
These were, however, collaborative ventures where the whole work evolved out of discussion and participation. What makes The Skriker new is that Churchill wrote the text on her own, then handed the play over to Spink and the composer Judith Weir to complete. It seems an astonishing act of trust for her to limit her control to the play's three speaking characters, leaving the other 13 performers (dancers, singers and a stilt-walker) to be turned into characters by Spink on the basis of her very sketchy stage directions.
Wasn't she ever worried that the final product would be wildly unlike her original conception? Wasn't her artistic ego ever threatened by these strange characters marching in and taking possession of parts of her play? Churchill gives the idea serious attention, smiles slightly bemusedly and shakes her head.
'I didn't feel possessive about what the characters should be like. It's nice not knowing what to expect. Anyway, I did originally base them all on these specific odd creatures from folklore, like Kelpies and Sprigens and Raw Head and Bloody Bones (a grin of relish), so all their stories fed into what the performers made of the characters.' Then a lovely smile: 'I think I'm very susceptible to performers, to falling in love with what I see them do with my plays.'
The decision to work with dancers in The Skriker had a basically practical motive. The play began as a straight literary work, with Churchill trying to create a magical form of language 'where the sense of the words would be constantly subverted by puns and rhymes, and where the verbalness of the text would be pushed to an extreme'. The story was pure fantasy, centred around a Skriker (a shape- changer or death portent), whom Churchill saw as a 'polluted, not-believed-in nature spirit who comes up to the world to get love, attention and revenge'. As the play progressed, more and more creatures burst out of the Underworld and Churchill found herself with a huge and unwieldy cast of characters. She decided she could tell the story far more economically by stripping the speaking roles down to three and by having the rest of the cast simply dance and sing.
Churchill doesn't, like some of the theatre establishment, regard dance as a dumb cousin of drama, and cherishes the different levels at which it speaks.
'Maybe it's to do with having been very verbal for a long time, but I find it very moving and interesting watching people doing without that. Dance can be so much more abstract and less literal than words.'
It is also more concentrated. She describes one scene late in the play where a crowd of businessmen are being preyed upon by strange creatures - 'all riding on their shoulders, twittering away. It's quite a short moment which would take much longer, be far more laborious, as a written scene'.
In the rehearsal, I saw the cast was working on a passage where a dead girl recalls the gruesome way her parents killed her. The words were sung by a 13- year-old schoolgirl, and were imaged by a dancer moving at the other side of the stage. Between them they set up a magnetic field of innocence and vulnerability that held and silenced the room.
Churchill watched this scene avidly ('I love this bit'). In fact, for the entire morning her attention rarely left the performers - all of whom put on a good show even when not strictly rehearsing. The dancers, like all dancers, didn't stop moving even when sprawled around discussing a scene, ironing out tweaks in their muscles, groaning masochistically over a stretch. The singers hummed little runs of melody. Katherine Hunter, who plays the Skriker, pushed her extraordinary tough little body through punishing exercises, pulling her face into a series of grotesque, rubbery masks.
The cast seemed as practical and undefensive about the whole project as Churchill - actors and singers learning how to move, dancers how to sing - and all concentrating matter-of-factly on resolving problems. Director Les Winters says they were lucky to get a group with 'such an appetite for this kind of work'. Churchill says she can't think of many actors who'd be happy about being surrounded - and often upstaged - by such a large group of singers and dancers.
But would Churchill herself ever like to go solo, to write a novel and have complete control over her own writing?
'I've sometimes thought I should try to write a novel but it just doesn't take life. I can't do it for more than a page without thinking this would be more vivid, more condensed, more intense, more exciting if it was some sort of play.'
She agrees there's more scope for impersonation, for flights of fantasy when writing for the theatre.
'There's something about the fact that a play is going to be an event, out there, which is very exhilarating, or freeing, or something . . .'
She slows down, frowns, seems to feel the subject goes too deep for interview gobbets and smiles: 'I don't know what to say.'
In rep at the Cottesloe, Royal National Theatre, South Bank, London SE1 (071-928 2252). Previews from tonight; opens next Thursday