Yeah, the US education store doesn’t do any sort of verification. I remember back in the mid-late 2000s (when I was still in college), Apple Stores asked for student ID (assuming you weren’t buying your stuff from the university bookstore), but were never super serious about checking it. Similar for employer discounts in-store.
I think Apple makes the US education store open because they also allow for parents of lower-education kids to get discounts and that includes people who home school and thus aren’t as easy to verify. Most student discounts in the U.S. are gated by verification services (so the alumni email or fake edu email trick doesn’t work anymore), but for whatever reason, Apple’s isn’t. I don’t know how common home schooling is in the UK, but that might be the difference.
I’ve used the education store consistently for the last dozen years or so for me or for my mom (who is retired now but who was an educator) whenever I buy a Mac or other big-ticket item. I used to use my employer’s EPP page on Apple.com (where they also do not check for online orders), but the education discount is better and you get to take advantage of back to school offers.