Who wanted to enrol in Alcoholics Eponymous under the name of Johnnie Walker? Certainly none of the characters in David Hare’s My Zinc Bed, for there are few if any jokes to be had here. It is a serious, not to say depressing play, as anyone who saw last year’s film version on TV will remember. The title refers to the metal drawers to be found in a funeral parlour. We shall know nothing, says one of the characters, until we are laid out on one.

The play’s concern is addiction, which either accounts for its presence in, or suggests a reason for the naming of, the Royal&Derngate’s brief Addicted to You season. We are offered lessons – yes, and sometimes we do feel we are under instruction – about mankind’s compulsive need for love, success, money, influence drugs and (the main area of inspection) alcohol.

The focus of attention is a 30-year-old poet and journalist Paul Peplow (Jamie Parker) whom we first encounter as he commences an interview with reclusive millionaire businessman Victor Quinn (Robert Gwilym). As things turn out, though, the latter is soon the one doing the interviewing. He early discerns Paul’s serious problem with alcohol, and his attempts to beat it though membership of AA. Victor does not approve of the organisation, considering it more of a cult than a cure. Laying down the law (he’s used to that!) he tells the young man: “You are not addicted to alcohol; you are addicted to blame.” He goes on to say that he knows someone who has ditched AA. We guess this is possibly for another dependence – on him.

So it turns out, for the woman, a former boozer and junkie, is his Danish-born wife Elsa (Leanne Best). We first meet her in Victor’s office, where Paul has been given a job knocking his prospectuses and the like into shape. Their mutual attraction is obvious at once, though its development puts serious strains on his determination to kick the hooch.

This is a powerful, intriguingly enigmatic play, whose subtleties gradually come to be appreciated as the action unfolds. Director Laurie Sansom takes things at a suitably steady pace, encouraging startlingly good performances from the three members of the cast. Sombre music, often distantly heard (Adrienne Quartley), contributues to the slight aura of menace, as does Jess Curtis’s studiedly gloomy design, suggesting a cross between a baroque mansion and a bar.

The play is packed with excellent observations and insights. I especially admired one on lying: “One need only do it once to spread infinite distrust.” But isn’t that one of someone else’s bright lines?

Until March 13. Tel: 01604 624811 (www.royalandderngate.co.uk).