I bet Robyn & Mitch are right, in which case you can probably Google up more details. One website says Ron Goodwin's music is splendid and the harpsichord-laden theme tune would become familiar as it was used in all the other entries in this series. But that web page doesn't give any further info about the music. Goodwin must have a site, which might help.

It could well be an old traditional melody that Goodwin arranged (I can't imagine your mother's music-box got it from him!) so if anyone catches a Rutherford/Miss-Marple film playing on TV, listen out. Don't know what the story is about online access to this sort of thing, but if you can pin one of these films down and post a link, you'd probably get an avalanche of replies. Will keep an ear out...