Michael Frayn's 2002 novel Spies is at once a compelling mystery story and an evocative celebration of childhood, its author's especially. Stylishly translated to the stage, in a co-production by Theatre Alibi and the Oxford Playhouse, it provides two hours of agreeable entertainment that is by turns witty, exciting and warmly nostalgic.

The wit, of course, is always to be expected where Frayn is concerned. His novels, journalism and plays have kept the nation chuckling over five decades. In adapting the book, Daniel Jamieson has naturally maintained its best lines. (A typical example: "Memory Lane, the last house before you go round the bend and it turns into Amnesia Avenue.") Kept, too, is the narrator - the novel is written in the first person - who is onstage throughout and looking back on his younger self, a lad in his early teens during the Second World War.

The smell of privet is the equivalent of Proust's madeleine in conjuring Stefan (Derek Frood) to the past. Hedges loom large in the plot as the hiding place from which Stephen (Benjamin Warren) and his pal Keith (John-Paul Macleod) spy on the latter's mum, convinced - well, perhaps not entirely - that she is a German spy. The boys are nicely drawn. While Stephen is a slack-socked scruff in the William Brown mode (he, too, has a screaming Violet Elizabeth in Cerianne Roberts's Barbara Berrill), Keith is a spit-and-polished little prig.

Why this is so is revealed when we meet his martinet of a father (Christian Flint), who is punctilious, precise and calculatingly cruel. Since, in Philip Larkin's words, "man hands on misery to man", all these attributes of character have been beaten (literally) into his boy - as well as his absurd taste for expressions like "old bean". With some doubling-up (even tripling-up) of roles by the six-strong cast, there is also the chance to enjoy Mr Flint's work in a very different part - that of Stephen's sniggering slob of an elder brother.

But if Just William is brought to mind in some aspects of the play, it is very much the flavour of L.P.Hartley's The Go Between that is found in others. This is a world in which young people stray - or are invited to stray - into the dangerous and uncharted waters of adult life. Just what is the delectable Mrs Hayward (Jordan White) up to? Clearly not spying, but why her mysterious daily visits to a railway tunnel in the neighbourhood?

As with the book, I confess myself somewhat puzzled by aspects of the play's denouement - an absence of acuity on my part, I suspect. Throughout the action, however, director Nikki Sved maintains the interest of the audience in the swiftly told tale. Especially felicitous is the use of live music - Lisa-Lee Leslie (accordion), Raphael Munton (cello) - to heighten dramatic tension and maintain the impetus of the story. James Cotterill's highly adaptable set, with its sliding panels and swivelling doors, serves well in this respect, too. I was less enthused, however, by its materials - corrugated iron that looks more suited to an urban wasteland than a well-tended suburban cul-de-sac.

While I wondered whether there would really have been electric trains running through the aforementioned tunnel in those days - just possibly, I suppose - I know beyond any fear of contradiction that no teenage boys of that time (of any time) would have left uneaten, indeed untouched, a plate of sugary Chelsea buns such as Mrs Hayward hands to Keith and Stephen.