Up here children start nursery school the September after they turn 3, so my son started September 2008. He goes to a state school and we had to submit applications in a certain month at the beginning of this year, but we also had his name on a waiting list for the application form for about a year before that - from the moment he turned 2 in fact.
Now we are doing the applications for infant/junior schools, but they only opened the application window about a month ago. The factors are not when you applied but whether you meet other criteria such as whether they have siblings at the same school or whether you live in the catchment area. I guess all areas are different, and I expect fee-paying schools are different again.
I suggest you speak to the Education department of your local council for the best advice, or perhaps the Health Visitor might know?