I needed to change the basin tap washer. I got a half inch washer out of
an old pack, but I was surprised to find that it doesn't fit. The tap
head has a sort of cup the washer fits into, and the washer is a bit too
big.

I'm pretty sure it's this one:
https://www.toolstation.com/shop/p45674

I suppose the correct washer size might be 3/8"? But then why is it
marketed as 1/2"? And in any case, I don't think the difference is as
much as 25%.