I’ve just checked out the Open All Hours ep mentioned where its said a scene of Granville dancing to Singing in the Rain has been removed. The one on Youtube I found shows this very scene (title “The New Suit”). Why they would leave this scene intact on early DVD releases, but cut it on later versions I don’t know. It’s a very memorable scene so it’s a ridiculous they cut this because of a bit of music. This rights issues stuff is becoming a joke. If you think the BBC are bad then try YouTube for their censorship.
I doubt that it’s censorship by the BBC. This is very likely a case of a licence expiring and they were unable to reach a financially viable agreement with the copyright holders for it to remain on subsequent releases.