Daysoftheweek - your comments about Angelachill intrigued me so much I had to go and read the whole thread!! Great laugh, she must be a west londoner !!
Once you have been granted a place at a school, even if you move, they are not going to take it away from you. So I would apply just before the cut off date and get your space. I assume your child starts next september.
When you move to final destination, contact the nearest school (school that you want) and explain you have moved. Provide a copy of the rental contract. You will get on the waiting list, and dependent on criteria should be topish of the list.
I went top of our waiting list. My friend moved this summer to new house and was third on waiting list and found out they got in end of summer term - her DS starts tommorrow!! Lots of people are moving like you, so hopefully you should end up with the right school.
When you have got your new place then contact other school and decline place. They will then open it up to someone else.
Also as your son is 4, he doesn;t need to start until 5 so if no place in new school you could always wait until a place becomes avaliable. In my sons year of 60 kids - three children left last year so we had three new kids.