We just got through the 11 plus process, so feel free to PM me.
It really depends on where you live and what the school's criteria is. We live in Orpington and have access to the Bexley grammars schools, Kent grammar schools and also the local supper selective grammar school called St. Olaves.
Bexley has its own 11 plus test which if you pass gives you access to the 4 grammar schools within Bexley. However, just passing the test is sometimes not enough as distance also plays a role. So if you're score is amongst the top 180 kids, then it doesn't matter where you live - if you choose a Bexley school then you're guaranteed a place. However, if you're not in the top 180, then it is based on distance. So someone living closer to school with a lower pass mark will get in as compared to someone living further away with a higher pass mark.
Kent: Kent has its own 11 plus exam for all the grammar schools in Kent (which are quite a few!) At a minimum, you need to pass the test to be considered for the grammar schools. However, whether or not you actually get a place then depends on each school's admission criteria. Some schools will go on distance, while others will have a fixed number of places for high scoring children (e.g. Judd and Dartford have some places reserved for children who have a high score and don't live in Kent - so distance isn't an issue as long as you have a high score. These schools are usually referred to as super selectors, as they tend to have their own cut off marks - just passing Kent test isn't enough, you need to pass it with a high score)
St. Olaves - this is also a super selective school and has no catchment. I know some children who will travel a ridiculous distance to get to this school. They have their own exam which is done in 2 stages.
Tutoring - based on my research, this really depends on where you live. Some areas have grammar schools which aren't super selective and just passing the 11 plus will get you in. If you're in such an area, then as long as you child in amongst the top of their class and understands exam techniques and does some past papers, they will have a good chance of getting in. Some tutoring may be beneficial.
However, if you're in an area with access to super selective grammar schools then it's a different ball game. Again, it also depends on where you live. For example, if you live within Kent and are within the catchment of a grammar school, then you only need to pass the test and any bright child with a bit of practice can do that. However, if you're outside catchment and are aiming for the handful of seats reserved for high scorers, then quite a bit of tutoring and practice is involved - especially if you're trying for a school like Olaves.
In an ideal world, everyone would sit the 11 plus exam and the paper would be based on what they have already learnt in school. But the reality is that schools like Olaves have questions on topics that the children would never have seen at school and the only way to crack that is through tutoring. At first I tried to fight the system as I thought having access to tutoring isn't what grammars are aimed at and it isn't fair on those who can't afford it. But I soon realised that my child would be the one left behind as everyone else around me seemed to have multiple tutors! We didn't go crazy - my son had a tutor once a week and didn't drop out any of his extra curricular activities, but towards the end we did ramp up a lot.
At the end, he got the school he was aiming for and it taught him the importance of hard work.