Peter Brook isn't an easy act to follow, but his daughter Irina is doing an impressive job

Irina Brook is the least portentous of people, but she's willing to admit that there is a fateful frisson to the mere idea of her directing A Midsummer Night's Dream. In 1970, her father, Peter Brook, directed the most famous production in the play's stage history. For most people who love theatre, the white box set, with its trapezes on which dangling fairies spun plates on bamboo poles, is an indelible icon, located in the collective memory and in the history books.

For Irina, who was a little girl at the time, it was an adventure playground upon which she would romp with friends. "A Midsummer Night's Dream is so much part of my childhood, my genes, my desire to be in the theatre everything!" she says, laughing. "And such an outrageous thing for me, as a director, to do!"

But now she has made that date with destiny and directed an infectiously joyous production with six male actors. It's not a self-conscious, weighty response to any supposed Brook family challenge (part of the delight is that it is unpretentious). Rather, in conjuring up a charming, knockabout company spirit, it creates a sense of family generous, chaotic yet controlled, ready to share publicly an intimate flair for fun. Her version, which runs for an unbroken 90 minutes, is called En attendant le songe. The framing idea is that the actors have got stuck in Athens airport because of a strike. Out of the goodness of their hearts, the team of builders employed by the theatre decide to put on the show so as not to disappoint us punters.

It's as though Shakespeare's mechanicals have been let loose over the play. But, miraculously, this does not mean that A Midsummer Night's Dream becomes a "Pyramus and Thisbe"-style romp, nor does it involve gazumping the amateur-dramatics hilarity of that climactic entertainment. Partly this is because Brook has gathered six idiosyncratic and sympathetic actors, who could persuade you of anything and switch the mood in a moment (aided by a persuasive lighting design) from giddy farce to heart-stopping wonder. And in its deliberately hectic, hand-to-mouth yet delicate manner, Brook's imaginative apprehension of the piece plays on the root meaning of the word "amateur". It proves that by generating an atmosphere of love, a show can make a ridiculous spectacle like Grald Papasian's Bottom, here a plumber whose translation to an ass is effected with the hardware of his trade (the ears two showerheads; the phallus a length of tube) look, at moments, like the most touching sight. Or it can, with equal plausibility, cast as the Indian boy a girl of five (Irina's daughter Maia) or a man in his early fifties who has hardly been on stage before.

With his RSC Dream, Peter Brook brought to completion one phase of his theatrical quest. He then moved to Paris where he created his international research centre, and to the Thtre des Bouffes du Nord, the former music hall that has been his base since 1974. It is here that Irina's En attendant le songe is currently playing before resuming a tour in France (and, if there's any justice, coming to London next Christmas).

The production of this "cute rags-to-riches story", as Irina describes it, did not, however, begin life at this august venue. It started at a little local theatre out in the sticks, near the 16th-century mill where Irina and her then partner had chosen to bring up their two children. It was commissioned by the tiny Festival Dedans Dehors, and intended to run for five al fresco performances.

Irina Brook's mother is the distinguished actress Natasha Parry, and Irina grew up wanting to be an actress too, which she did after training with Stella Adler in New York. It was only in the mid-1990s that she turned to directing, with Richard Kalinoski's Beast on the Moon at the BAC, which went on to great success in France, winning five "Molire" awards (including best director). Brook was then invited by the legendary Ariane Mnouchkine to work with her Thtre du Soleil.

For them she created a French- language All's Well that Ends Well, a play she had previously directed in English for the Oxford Stage Company. Further awards and offers followed. There were operas, too, but by the time the call came from the Festival Dedans Dehors, Brook says she was at the end of her tether. The rural idyll she had hoped to create for her children had foundered (unwelcoming locals, no social network). She realised that she was accepting big work offers "just to fill my diary".

What she wanted was a communal set-up where she could create work near and with her family. She's a Brook, which is a great gift and, like all gifts, an ambiguous one. "The problem with this kind of family and upbringing which I can see my children inheriting is that you become rootless." On the other hand, there's that strong, principled, and characteristic sense that theatre is meaningless unless it strives to be life-changing. So there's a paradox in the predicament of this woman who went back and forth from home in France to school in England. And hence, her reinvigoration by En attendant le songe, which allowed her "to cast actors equally for their human qualities as theatrical abilities".

Hence, too, her decision to move to Massachusetts to work in a Shakespeare theatre that will provide that sense of community for nine months of the year and allow her to develop her French company during American school holidays.

One thing Irina she has inherited from her father is a sense of humour (an aspect of him that is rarely written about in portrayals of the "guru"). And this seems to have been passed on to her children, too. When I asked little Maia whether she would be playing the Indian boy at the next performance of the show, she shrugged in a "Search me, but that's showbiz!" manner. Her turn next.