I think that most state schools are ok as long as you avoid the bottom sets.
I am not a primary expert at all but I do think lots of reading and establishing basic number confidence is really important before they go to secondary.
The problem is most children just don’t see learning as their job; they think teachers will do it for them. This is even a problem in private schools: there are just more staff and more time to do clinics etc.
In an ideal world, by mid Year 10 a pupil should have some idea of their course, how to look up the syllabus online (it is really easy) and how best to revise. If they get this, they can really help themselves. I also think that buying them a full set of text books (and showing them how to use them) is tremendously helpful. When you are lost in a prep, being able to go to the relevant section of the textbook can really help.
Parents need to keep on top of how their children are doing and proactively liaise with the school if they are not fulfilling their potential.
On top of this I think regular chats about what A levels they might do, what they are thinking of as a career etc are really useful.
Pupils need to feel both valued for their efforts but also made to work to do as well as they can.
There is no magic bullet but private schools are not miraculously good, nor are state schools (on average) as bad as some fear. Private schools are really good at doing all the above but there is nothing good parenting (and maybe a little tutoring, but not much) can’t replicate.