I understand what posters are saying about crushing children at such a young age. I can see the problem with not be "picked" for grammar school if you are keen.
My DD is in year 6. She goes to a rather genteel CofE school. Daffodils in the church yard, duck pond, prefects, house system, middle class catchment, etc.
Being at the top of the class is not so much fun for her. The fact that she "knows everything" immediately has not gone unnoticed by her classmates. Quite a few take it personally. They get their digs in. They get their digs in every. single. day.
If she tries to hang back, the teachers tell her off for not trying. If she tries to join in the sports and be "one of the gang," she isn't picked by teachers because other kids need their chance to shine. She misses most play times because teachers have her running errands and doing special jobs all the time. This further irritates her classmates. She would actually like to be playing outside instead.
She spends a lot of her time in the classroom helping other kids, which is fine on the face of it. But it further reinforces that she is "different." Some times the classmates she has been told to help feel humiliated to have another child trying to teach them. They can't retaliate on the teacher whose idea it was, but they can lash out at DD who would never have presumed in the first place.
Things were fine in infants. She started to seem ahead in year 4, but not wildly so. By the middle of year 5 the gap was widening. Now it's gaping. Our local comp doesn't stream at all year 7, and only for maths after that. I can only assume the trend would continue and the situation would worsen if we chose to send her to the local comp.
We've decided to send her to a selective private school. If there had been a local grammar school we would have gladly saved the swinging cost. What we really need is for DD to be considered "normal." We need her to be treated like a child because she is a child. She is emotionally and socially a child and needs to be seen and treated as such by her peers and teachers.