According to the Times Online, the most popular nursery rhymes in the UK are:-
1) Twinkle, twinkle little star
2) Incey Wincey Spider
3) Round and round the garden
4) Baa baa black sheep
5) The grand old Duke of York
6) If you're happy and you know it
7) Humpty Dumpty
8) This little piggy
9) Ring a ring a roses
10) I'm a little teapot
(What? No Lavender's Blue, Mary had a Little Lamb or Hey Diddle Diddle!)