Singing Together was of course the origin of Big Brother. All schools who took the broadcast had the right to nominate their 3 (I think) favourite songs; those songs that did not get enough nominations (usually the quiet ballady ones) were voted off and did not appear in the final broadcast of the term when all the loud, in-your-face songs were sung.

As to Old Roger Is Dead, in my (Suffolk) neck of the woods, being the Apple Tree was not a safe option, because it was progressive. The Old Woman selected the Apple Tree, and went on to receive her clout from Old Roger. Then for the next round the Old Woman became Roger, the Apple Tree became the Old Woman, and Roger dropped out, back into the general circle. So the new Roger handed out the clouting to the person they had originally nominated as the Apple Tree.