Ranger Steve, the second song you mentioned was "Don't You Want Me?" by the Human League (hit in about 1985/86, I think. I can't remember cos I was only 1 or 2!!!)

My nominations as WORST SONG EVER go to ....
Bob The Builder for both of his singles
Teletubbies for "Teletubbies say Eh Oh!"
Tweenies for any song that they've ever done!
Aqua for "Barbie Girl" and finally...
Spice Girls for "Wannabe"

And the winner is....(rustle of paper as she opens that gold envelope they always keep the results in)...TELETUBBIES FOR "TELETUBBIES SAY EH OH!"! Come on, Teletubbies, come and get your heads kicked in for making the worst record ever!