Yes, most gravel bikes wouldn't be allowed to start anything under UCI rules, not sure how rigorously the three peaks adheres to them these days. And CX runs *everywhere* in the UK, there are leagues pretty much everywhere, COVID has knocked a big chunk out of it, but the calendar was rammed last time I looked.I never see any of the other cyclo cross races, because apart from the Three Peaks event, they're not run in areas I usually visit. And in any case, if 33mm tyres is the regulation for cyclo cross, quite a few gravel bikes would be disqualified.
Surely it depends how rough the trail is. Some trails and canal tow paths are so smooth you could take a road bike with 25, or even 23 tyres. Other off road trails would be awful on narrow tyres.
And FWIW, I live in the middle of what is pretty much ancient forest, on granite, so it's all rocks, roots and orrible crap.