This is the Berceuse or cradle song from Faure's Dolly Suite arranged for two mandolins by Cliff Doust. It is also the theme tune to "Listen with Mother" a BBC radio programme that we all listened to when we were very young.
Brilliant. With wit.
I was going to say I'm not old enough to remember this theme tune but I recognised it immediately so maybe I am. Rather disturbing towards the end - it'll give the kids nightmares.