Tony Cownie isn't letting the grass grow under his feet.

The acclaimed theatre director ended 2012 with a superb staging of Liz Lochhead's version of Molière's Tartuffe at the Royal Conservatoire of Scotland and another highly successful big-stage pantomime, Cinderella, at Glasgow's King's Theatre. As if to prove his versatility, he begins the new year with a production of Shelagh Delaney's classic kitchen-sink drama, A Taste Of Honey, at the Lyceum in Edinburgh.

When we meet, I ask him why this play – written by a 18-year-old girl and first staged in 1958 – continues to be of such interest to theatre makers and audiences alike.

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"It's just a great piece," he says of the drama, in which Jo, a white teenage girl in Manchester, gets pregnant by a young black sailor while negotiating a torrid relationship with her mother, Helen, who is more interested in alcohol and lucrative relationships with men.

"It's really good about women and motherhood. What is a 'mother'? What's expected of a 'mother'? Still today, society has such preconceptions about what a mother would and wouldn't do."

For Cownie, there is something enduringly relevant and continuously dramatic about the central relationship between Jo (played by Salford girl Rebecca Ryan, of Channel 4's Shameless fame) and Helen (Lucy Black). Simultaneously antagonistic yet co-dependent, it resonates in the daily lives of today's audiences. More than that, it carries a dark, biting humour which makes for a bleak kind of entertainment.

"Helen's a very funny character," says the director. "We find ourselves laughing in rehearsals. Lucy Black asked me, 'but should we be laughing at this?' And I said, 'absolutely!'. Helen says the most terrible things, but they make you laugh. That's part of Delaney's weaponry as a writer. The worst things are said as jokes."

Cownie is keeping the play very much in its time and place (Manchester in the late 1950s). The set design – a revolving stage containing a hyper-realistic representation of Helen and Jo's depressing digs and the street outside – will sit in stark contrast to the opulence of the Lyceum's gilded proscenium arch.

Likewise, the dark comic tone will remain true to the spirit of the play's first producer, the great Joan Littlewood (whose production is of far greater interest to Cownie than Tony Richardson's famous 1961 film version).

"In the end, the play became a lot harsher than it was originally written by Delaney," he explains. "For example, it was Littlewood who said that the character of Peter [Helen's 'fancy man'] should be a sleazeball, rather than the more sympathetic character Delaney had written."

Add to this Jo's friendship with Geoffrey, who seems to have been evicted because his landlady thought he was gay, and you have, to Cownie's mind, a drama which is brilliantly written (and surprisingly so, given the youth of its author) and bravely political.

"Delaney's really fighting a social battle single-handedly. The play encompasses and defends so much, whether it be in terms of saying it's OK to be gay, or black, or a teenage girl who gets pregnant outside of marriage. As a director, you feel a real responsibility to maintain the authenticity of the play. This is written by an 18-year-old about being young, in Manchester, in 1958. You've got to maintain the authenticity of that voice."

A Taste Of Honey runs at the Royal Lyceum, Edinburgh, from Tuesday until February 9,