7+ registration usually closes by Sept/Oct for the schools you are looking into; check websites for latest info. Reading is the key to success at any school; would ensure he understands what he is reading and enjoys it. Observing his surroundings and being able to make judgements is also a key skill; look at book covers and form opinions what the book is about; look at the paper and see what he can see. It's a process that takes time.
You need to ensure he is able to write neatly; knows sight words and spellings; know his times tables cold: 2,5,10,3 by mid of Year 1, and then continue to build on the others by the end of Year 1; know all the spellings; is reading fluently- ideally starting chapter books around spring; can do basic arithmetic with accuracy (speed will come later)- Schofield Sims First Mental Arithmetic books are brilliant for this. But before you start him on these, try Gold Stars basic maths books or Carol Vorderman age 5-6, 6-7, or any other simple books, etc. Also if you get him through the Bond VR, NVR books up till age 6-7/7-8 by Jan (Bond is rather easy, hence tutors in the know do not depend merely upon these), he will be in good stead for actually preparing for the tests, rather than learning the foundations for the tests. In addition, if he is exposed to other resources such as The Week Junior or other magazines, it will help immensely expand his abilities (it has some interesting articles, as well as puzzles that I highly recommend to students till 11+).
This may sound like a lot (& certainly don't intend to scare you), but school will be taking care of most of the things mentioned, if your child attends indep. You just need to supplement what they are doing. Just that extra bit of work every day and he will thrive.
subscribing to Reading Eggs and the maths app of the system - I am sure there must be more recent apps; but used these for my own children at that age. Something that does not feel like work to boys, works wonders.
I hope this helps.