Talking of background music, I've been hunting down the name of this track I first heard during the slides on a BBC Children's compilation VHS I had when I was very young, and heard again in a Jackanory documentary from 2006, both Shazam and AHA Music haven't been able to identify it, so is it safe to assume this is library music?
As a general rule if Shazam and similar apps don't recognise it, its almost certainly library - those apps are more geared toward mainstream music. There may be a small chance it probably isn't library, but you have a clean copy of that music from somewhere else, you could upload it to YouTube (as private/unlisted, you can always remove it later), and see if the copyright bot scanner can ID it. YouTube can sometimes ID library music (it recognises most if not all of the themes used in Zzzap! for example, which used nothing but library music throughout its run), but if it has speech over it as is the case in that video, it'll struggle.