If you are in a state primary, and want to send your child to a selective secondary school in the London area, expect to supplement.
We live in outer London and the tutoring traditionally started in year 5. It seems to be creeping into year 4 now. Perhaps to secure tutors, more than anything else. That said, we started the summer before year six, and it worked out ok. It was a little stressful though. I wouldn't recommend waiting that long.
All these selective tests are "knock out tournaments," not "qualifying exams." They have limited spaces and an abundance of able children. So if you want one of the most "elite" schools, prepare for an endurance test, even if your child is naturally bright.
Also, looking around, I notice that prep school kids are using tutors too.
As for the non-academic stuff, you will probably have to run your child around after school to dance, drama, tennis, swimming, gymnastics, football, hockey, etc. State primary schools offer some of this, but at our school (a leafy, honey pot CofE school) they cannot offer enough for everyone. There are children who would like a chance at cross country, netball, tag rugby etc. but don't get chosen. They can only run one team because it is all done on a volunteer basis. So many children who would like to participate are let down.