Apple publishes education prices -
https://www.apple.com/uk-edu/shop/buy-mac - you’ll need to verify employment or education status in the usual way to order.
As mentioned, there’s a £100 discount on a Mac Mini but also 10% off any upgrades when configuring BTO.
My partner works for the NHS and she gets a discount that looks the same as mine (I worked at a university). She uses Blue Light but also uses a NHS discount online service (she’s found that what’s listed at BL isn’t always up to date - I know Apple used to do a discount for that scheme but not sure if they still do). Also, she’s got a discount in-store (one time it was buying an something for me that I didn’t think would get a discount - think it was a third-party case - but when she asked about NHS it did).
Also, in my experience, UK premium resellers also offer some kind of discount (and sometimes better than Apple) so companies like
https://www.krcs.co.uk/nhs-discount can be worth contacting.