As far as I know the only schools that have selection for reception parents is Thomas's and you'll already know if you're a Thomas's parent.
If you're really not sure there is a simple test you can perform to check.
1) Look outside, do you have a new 4X4 parked outside?
2) Look in the mirror, are you blonde and thin?
3) Look at your children, are they the annoying/confident/assertive/pushy (delete as appropriate)
4) Look at your calendar: does it have the weekends marked out with "staying in country"
I am being cheeky, and I hope Thomas's parents take it in jest, but if that list fills you with horror versus you thinking "that's ok, some people live like that" then you'll know if you want to go to Thomas's.
The others are more about getting names down on a list as soon as possible.
For the 11 plus all the schools do selective entry and EVERYONE tutors their kids.
The common refrain seems to be "Little Johnny isn't really being tutored but he loves the teacher so much its more about having fun".
Seriously, I heard that one once!
I am slightly ahead of you in the system and this seems to be the overview:
1) Private reception places, don't bother tutoring, get on the lists.
2) Private 11 plus. Start tutoring at the start of year 5 and tutor like you've never been tutored before.
3) Don't listen to anyone in year 5 who kids are hoping to go private who says they're not being tutored. Unless they are at the top end (and there is only one kid per SCHOOL in this category) or at the bottom end special needs) then they're probably lying.
Hope this helps.