Probably depends on the country. Here in the Netherlands the difference of quality is really small between public elementary schools. Private schools are practically non-existent.

Outside of primary schools with a very strict religious background they are really all the same. You don't look at those with exit metrics and average scores on national tests the way you do with schooling after it.

Middle and high school do matter, but I don’t think primary/elementary/grade school — whatever you call it — makes much of a difference. I attended the average neighborhood primary school back in my day, and went on to the most competitive middle school, high school, and university.

Are you really implying a school in Croydon, a large town in south London is going to be functionally and qualitatively equivalent to say a school in Golders Green, an area in the London Borough of Barnet? [1][2]

Equivalent in all the areas one might measure the attractiveness and potential of a school?

[1]

https://en.wikipedia.org/wiki/Croydon

[2]

https://en.wikipedia.org/wiki/Golders_Green

edit:typo

You've linked to the wrong wikipedia article, and used the word "town", which leads me to think you don't understand London much.

Is there any reason you linked to wikipedia articles about a part of London with a large Jewish population vs a part of London with a large ethnic minority population?

https://en.wikipedia.org/wiki/London_Borough_of_Croydon

I just realized that. Yes the one you linked is the one I meant to use in my example.

I meant to pick a town/neighborhood with rich inhabitants (per capita) and a town/neighborhood with not so well off inhabitants.

I know nothing about schooling in England, but I would imagine the parents’ education as well as socioeconomic status plays a much greater role than elementary schooling, as is the case everywhere else.

I live in London, and I don't get your point. There are OFSTED Outstanding-rated schools both in Croydon and Golders Green.

The UK is a pretty poor example since it's a very elitist country.