There are lots of private schools in south Manchester/east Cheshire. For single sex, look at Altrincham Prep (juniors only), MGS (junior and senior)
For co-Ed, Cheadle Hulme School (junior and senior), Hale Prep (smaller, junior), the Ryleys (junior), Kings Macclesfield (junior and senior), Stockport Grammar (junior and senior), wilmslow prep (junior), Pownall Hall (junior), abbotsford prep (junior), st bedes (junior and senior), moor allerton prep (junior)....
I think you need to decide whether you want a smaller school or a larger one, or whether you want to try to avoid your son having to sit the 11+ entrance exam. All of the above schools have good reputations but they are all different in terms of size and facilities. Some are selective and some are not.
My children go to one of the junior prep schools I have named above. It is non selective and has around 200 pupils in total so they get a very individualised experience. It has good facilities (not as amazing as some) and they have great academic outcomes with the vast majority of children going on to the selective secondary school of their choice. I chose it because of its location (I bought a house first, then looked at schools, rather than choosing a school first) and because of the feel of it when I looked round, and it’s reputation. It is a diverse school with lots of nationalities represented which I like (although we are English, I like my kids to see diversity and interact with children of different backgrounds).