My memory turns out to be pretty good as regards content. Thanks to Google and IMDB I learn that the play was "Girls and Boys Come out to Play", and it was part of a series of thrillers that was indeed called Menace. Date is another matter: it was actually broadcast in 1973, when I was ten years old. (What was my mother thinking of?) It was repeated the following year, but not as part of the Menace series, so I must have seen the earlier broadcast, I think.
Now, of course, I wish I could watch it again - and it seems I'm not alone, as these discussion board conversations make clear. It appears to have been deleted, but there are tantalizing rumours that it may still exist somewhere at the BFI, possibly misfiled, or possibly (like the original tape of The Wicker Man and our homicidal heroine's little friend) buried under a motorway.
Does anyone else remember it?
Also, isn't it time we all faced up to the fact that everything good and memorable dates from 1973? From this play to The Wicker Man itself, to The Dark is Rising, to the first ever episode of The Tomorrow People (how well I remember that!)... Bliss was it in that dawn to be alive, and to be ten was very heaven! Penda's Fen was broadcast the following year and was a splendid effort, but already the sun was setting on that golden age. Picnic at Hanging Rock, the year after that, was almost too late. Shades of the prison-house were closing in the form of Johnny Rotten and the temporary madness of all my friends, and in their spikey wake trailed the '80s, Mrs Thatcher, The Human League, and thirty years of hurt.
I cling to the memory of that little homicide as to a floating spar.