I've been working in education for a very long time and personally I'm not convinced that there's much point paying for a prep instead of going with a state primary if you're in the catchment of a good one.
Generally speaking, fee-paying schools have smaller classes and better facilities. Having said that, some independent schools can be pretty squashed into small spaces (more common in central London) and some state schools do have lovely grounds and heated swimming pools etc (especially in affluent suburban areas). Similarly, many state schools offer one-to-one music tuition and run a range of afterschool clubs.
Independent schools often have better wrap around care so it might suit parents who work long hours but they also tend to have a lot more holidays than state schools so more childcare is required then.
There are also some parents who (mistakenly) think that paying the fees means that they can be a bit more hands off with the education of their children because the school will sort it all. In reality, I think that the best performing children are the ones with the right ethos and encouragement/expectations at home.
For some people it can be a bit of a class thing, too with independent schools seen as a way of advancing in the social ranks.
I don't know if you've had a look at some official info, but you can find out a lot here:
www.compare-school-performance.service.gov.uk/
MIght be quite useful in addition to visiting and speaking to other parents.
But anyway, opinions on whether it's worth paying do range a lot and a lot of those who can easily afford fees are perfectly happy to go with their local state school (especially for primary but secondary is often a different kettle of fish). On the other hand, some people will really scrimp and save, give up holidays and drive a very old banger to pay the fees as they feel very strongly about the matter.