SaHD. I am not weird, but you might be ungallant.
Lots of all class parties adn relatively small classes, so you knew everyone. And a bit like how Londoners all know which (suburban) school Boris Johnson went to, but don't know which London school Sadiq Khan attended.
Thinking about it, its odd. Oxbridge people tend to say " when I was at Oxford..." rather than "when I was at University..." which then seemed to lead onto a chorus of "which college..", in the same way as others (or more often, the same people) would say "when DH was at Eton..." I did not go to Oxbridge and was struck by this, so a bit like Cleo, I was interested. But it was only one class in one year, and would not happen again as London has become a lot more international.
The same applied to Paulina's. I might know which schools friends who attended London Day Schools went to, simply because it came up when we were considering senior schools and often after having known them for a while. They probably do not know where I went. However five mums in DDs year at the same school were Paulina's. I was not close to any, but somehow it would get mentioned. (And remembered.)
Presumably that is part of the private state debate. That you have an answer when asked "what school..."