As far as I am aware LA schools do not hold wait lists for years 1-6, nor does the LA. The wait list system applies to the entry points only, i.e. reception class. This does differ for academy-run schools like Dulwich Hamlets and free schools like Judith Kerr who organise their own admissions. When you call the school they can tell you their current availability only, which is why it does pay to call your preferred LA schools fairly regularly. The LA have an obligation to allocate you a school place within 6 weeks of applying for an in-year place, and you are allowed to name just one choice on the form, but if no place is available they will allocate you a place anywhere. If you have found availability at one of your preferred LA schools, it is much better to let the LA know that so they can call the school and confirm it. Confusing yes, but that's the way it is. Good luck.