Ten years ago the ascent of Marianne Elliott would have been explained as part of a larger shift. Nowadays many theatres are controlled by women, while no director bosses the box office like Phyllida Lloyd with Mamma Mia! or Julie Taymor with The Lion King. So is there anything especially notable about Elliott’s elevation?

Only this: since her revival of Ibsen’s Pillars of the Community in 2005 at the National, Elliott has transplanted Zola’s Thérèse Raquin from page to stage, breathed fresh life into St Joan, given the premiere of Simon Stephens’s play Harper Regan, about a runaway housewife, and updated Ibsen’s Little Eyolf to 1950s Kent in Samuel Adamson’s Mrs Affleck.

As she turns to the riddle that is All’s Well That Ends Well, it becomes clearer that, more than other female directors, Elliott’s presiding interest is in women and their relationships. Women flock to her productions to see their own sex explored, men to see them explained. Not that Elliott will admit to a plan in any of this.

“I don’t do it consciously,” she says. “I don’t feel I understand my own gender. But I do find women constantly surprising and awe-inspiring. I don’t quite know why. Ultimately you’re just working away at a knot to try and solve something.”

Of course this post-feminist through-line would look all the starker if Elliott were not also behind the theatrical miracle that is War Horse, now stabled in the West End. Adapted from Michael Morpurgo’s children’s book, set among the trenches of Flanders and featuring staggeringly realised lifesize horses, it hardly seems Elliott’s sort of thing. She didn’t think so herself at first. “I thought, ‘That’s just impossible. We’re never going to do that . . . OK, let’s do it.’ ”

With Tom Morris sharing the direction, the play was workshopped for two and a half years. The result was awards galore for its designers and puppeteers. This is no coincidence. What with Anne-Marie Duff’s Joan of Arc and Tamsin Greig’s Beatrice, Elliott has a gift for nurturing prize-winning work from her collaborators.

It was that intoxicating account of Much Ado About Nothing for the RSC that fully showcased Elliott’s talent for seduction. Though Much Ado’s saucy Cuban flavouring was entirely her own recipe, she modestly presents it as a pragmatic accident. “I can’t remember how it came up. I remember thinking it should be set somewhere exotic that has a lot of music, which is what Italy represented in Shakespeare’s day.”

Will she also spin gold from All’s Well? Shakespeare plucked the plot from Boccaccio. The humble-born Helena falls for Bertram, the countess’s son. Undeterred, she follows him to the French court where, in return for curing the King, she is granted a wish. She duly wins the hand, but not the heart, of Bertram, who dashes off to Florence to fight wars and bed women.

As associate director at the National, Elliott was asked by Nicholas Hytner if she’d like to have a crack at another Shakespeare. She chose the play partly because she had never seen it. “It’s lovely to come fresh to a Shakespeare. You’re just so sick of quite a lot of them or you think, ‘How could I possibly do it differently?” The plot’s mixture of fairytale and modernity was also tempting. “This girl is following this boy relentlessly when he’s just not into her. It occurs all the time. Girls are particularly good at that. ‘Will he ever look at me? Will he take me on?’ It shows people’s attitudes up quite a lot. Everybody has a different opinion about whose side they’re on.” So is it Shakespeare’s Oleanna, the Mamet play about gender politics that notoriously split couples down the middle? “I hope not. I don’t like Oleanna.”

This is a rare dose of assertion. Elliott is just under 40, with a daughter of 4. With her legs curled under her on the sofa, her soft voice and demystifying patter, there is nothing of the directorial alpha female about her. “I’m not what you might expect a director to be. I’m quite a girly girl. But a lot of directing is being quite maternal. If you want to empower people, you should do it from a place of generosity and care.”

In the beginning she ran a mile from theatre. Her father, Michael Elliott, co-founded the Royal Exchange in Manchester; her mother is the actress Rosalind Knight. “I made quite a point of saying to my parents that I didn’t want to go into it.” She still doesn’t know why she read drama at Hull soon after her father’s death. Having gravitated into casting in television, at 27 there was a choice between jobs at Granada or the Open Air Theatre in Regent’s Park. She plumped for going about her father’s business.

“I think I needed to find it for myself. Although it was a terrible thing for me to have my dad die, it was ultimately quite releasing. For the progression of the race we want to be better than our parents. If they are really good at what they do then it’s unlikely.”

A year later, despite lingering acrimony between her family and the Royal Exchange (“there was some weird shit going on between my father and the other directors”), she even went back to his old theatre. In eight years she directed everything from As You Like It to Port, Simon Stephens’s play about Stockport, where she grew up. “I just found it utterly flooring. It was about moving on and leaving difficult things behind you.” Having already nipped south to stage Lillian Hellman’s The Little Foxes at the Donmar, she moved away permanently to the Royal Court as associate in 2002.

What next for Elliott? “Oh God, I’d love to do a musical,” she says, before remembering that she’s already in the early stages of creating one for the National, based on George MacDonald’s Victorian fairytale The Light Princess, with songs by Tori Amos. Meanwhile her tenure there is secure, at least for as long as Hytner is in charge. His successor “may not be wanting me to be around”.

She could of course run a building herself. “No!” she says. “Literally, no. I think you have to be married to that job and I’m married to a man, I’ve got a child. I’m not the right person for it. I have not got the right head.”

All’s Well That Ends Well is previewing at the Olivier, London SE1 (020-7452 3000, www.nationaltheatre.org.uk), and opens on Thursday

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