The only problem with putting their names down on the day you come home from hospital is this.
So far as I can see, most preschools arrange their waiting list in birth order (in fact, the 'model' admissions policy available from the PLA states 'we will arrange our waiting list in birth order'). Therefore, as places become available, preschools look on the list to see who is the next child turning 3 and becoming eligible for their nursery education grant. This can mean that if your child isn't 3 until the summer, all the places for that year have already been allocated, even if you've had your name down for ages.
Preschools are aware that this is a problem, but preschool committees have a choice. They can either do it this way, or alternatively they can save places for children who had their name down first, but it means the place could be empty for half the year, not generating any income for the preschool.
Either way, the system is inherently flawed.
The only time I can see a real advantage to getting your child's name down early is in nurseries that have a single intake each year, e.g. they admit 25 children in September and take the first 25 that registered with them.
Good luck finding a place. I'm a preschool administrator and our waiting list certainly suggests that 2006 was a bumper year for babies. But I would definitely second what nancy75 said about people hedging their bets by being on half a dozen waiting lists.