Holiday In Davos is a big favourite of mine, I sometimes play it on my radio show (I think it was you that introduced me to it, actually!)
Other examples I can think of off the top of my head:
Music To Drive By (Alan Moorhouse)- originally recorded by the Oscar Brandenburg Orchestra on KPM's Radio Program Music series, commercial version by the Joe Loss Concertium, arranged by composer Alan Moorhouse
That's Where I'll Be (Ray Davies) - instrumental version by Ray Davies and the Button Down Brass, vocal version by The Cavendish Chorale on Cavendish Series 10
Pandora (Ray Davies again) - original by The New Dance Orchestra on Cavendish Series 1, covered by Syd Dale's New Elizabethans for Rediffusion Reditune
Theme From A Serenade (Ray Davies again again) - original by The Ray Davies Orchestra on Cavendish Series 1, cover by The In-Keepers
There are a few library tracks that were re-recorded for BBC Radio sessions as well - there are alternate versions of Hawkshaw and Mansfield's 'She' and David Lindup's 'To Hounds' on a BBC Transcription series called Music Roundabout (presumably culled from sessions for Radio 2?), and Ray Davies (again again again) did a few by various composers including himself on his radio sessions.