Locally (not London), there are 2 types of private primary / prep schools.
Type 1 goes up to 11, and their chief raison d'etre is to prepare children to take the 11+ to enter state grammars (of whom there are a few locally), with a sideline in sending girls to the local all girls private, which obviously starts at 11.
As local state primaries are good, and the grammars draw mainly from state primaries (so having done e.g. more languages or separate sciences isn't critical when starting secondary), there is little advantage of such primaries over and above state school + 11+ tutoring (at home or professional). Unless, of course, your child is the type who will genuinely need 7 years of focused preparation to stand a chance of passing the 11+ OR your picture of 'a good education' is children in immaculate uniforms sitting in silent rows of desks being talked at by a teacher and taking dictation using a fountain pen...
Type 2 go up to 13, and are attached to the traditional 13+ entry schools, which are now mixed but were boys' schools. They take extra classes in at 11 - one of them I believe doubles in size at that point - but they do offer some advantages IF a child's eventual destination is the senior school attached - almost automatic transfer between schools, an extraoridinary amount of sport (the senior schools have poorer academic results than the local comprehensives but their sport is VERY impressive) and some subjects - e.g. Latin, languages - that a child transferring at 11 or 13 would have to pick up.
So I would start from a secondary school choice, and work backwards, thinking about when the 'big' entry points are e.g. 7+? 11+? Locally, I wouldn't bother with the 'to 11' privates unless I happened to live in one of the few areas with a genuinely poor primary, and would only bother tranbsferring to the 'to 13' preps at 11, because that is such a big entry point locally (they scoop up 11+ grammar school failures from the 'to 11' privates, as well as state school pupils looking to go to the senior schools)