Do I mention things that I achieved at primary school in my statement?

This depends on what you may be mentioning, and how significant it is to your choice of studies and career. For instance, if you performed CPR on a friend at the age of nine and this encouraged you to go into Medicine, then this would be extremely relevant to your statement. However, if you were awarded a Blue Peter Badge for that brilliant story you wrote when you were six, and are applying to study French, perhaps that is something you can remain proud of but not include in your statement. Try and include things that influenced your decision to study that subject and not things which are impressive but not very useful to you.