wysisyg, 'fanny' in UK is the vulva or vagina. Also called 'foof' 'noo-noo' 'pussy' and many other words. (I'm a bit too old to know all the latest urban argot.)

The backside is called 'bum' 'arse' 'derriere' 'rear' etc. But never 'fanny'!

But I still think altering the text of much-loved literature is bowdlerisation at its worst. If a girl is called Fanny or Titty, honi soit qui mal y pense!