[poizan42]

You need to actively defend a trademark to keep it protected. Formally registering it is neither sufficient nor necessary.

Also as someone pointed out on Twitter it's probably not even in the right category to protect against the use in educational material. Also even if it were it's probably nominative fair use anyways.

[petercooper]

I broadly think you are right, but there's an added layer of complexity here: UK company naming law. You can't even use words like "British" or "Royal" in your company name without meeting various conditions, so using anyone else's trademark is definitely out (and it's very easy for said holder to object without being subject to having their use of the trademark interrogated).