I read with interest about London prepreps on this board, started a thread myself once, and was told in no uncertain terms that the "you have to put your name down at birth" rumours were a myth. Was even told that the schools always had places and were desperate for people to go.
So, just rang around anticipating a move later in the year and want to start looking for a property and school... and they are all full. Indeed one of them actually said the words "you have to have your name down at birth as we are oversubscribed".
It is not a myth.