Ok so tutoring will not mean your child won't keep up in a grammar, there is research to show that does not happen.
But really check your current state school.
My child has been tutored by an excellent maths tutor who helpfully explained to me that my year 5 child had not been taught what he would have expected a year 5 child to learn.
So ... we have had to go through so much work just to cover what should have been covered. And yes, we were always told our child was brilliant and near the top of the class. I am finding the same for English and grammar type questions.
Also private schools prep much more for the 11 plus. I would not discount the advantage that a child in a private school has over a state school child at primary level. Ofcourse there are brilliant primary state schools but anectodally private schools have really been ahead of the curve when it comes to lock down so I think the gap will be wide both this year and next.
Really check the requirements, if you are applying out of area the competition is very tough and it is also tough in area.
Also consider your child and how they learn. My child is very bright but he is not quick and feels pressure. I am not sure I will even let him sit 11-plus as I am not sure I want to speech coach him.
You have had a lot of good replies already.
Do not underestimate the work involved to get a grammar place. Nor the cost of tutoring.
You also need to really familiarise yourself with the tests and layout etc
Personally I have found people lie about not being tutored. Yes I hear the phrase well of the kid needs tutoring they should not be in a grammar.. from my friend whose child goes to exclusive private prep that has extra sessions like speed maths and maths clubs after school.. 


Also it is a good idea to try get from you school the standardised test scores of your child.
Good luck.
I find the whole system deeply unfair.
Round where I live yep the tutoring starts at year 3 softly and ramps up in year 4 and 5.. and some people have a maths and English tutor and then do holiday courses all the way through year 4 and 5.