Interesting one this. I'm not from that area but the description reminds me of reports I've seen from the Harewood estate side of Leeds, people hearing something big moving through dense woodland at night, heavy footfalls, branches snapping at a height that rules out fox or deer.
The thing I always try to nail down with these reports is the sound pattern. Is it rhythmic like a biped or more of a lumbering four-legged gait? Makes a massive difference when you're trying to narrow it down. Could be a wild boar - they're expanding their range in Yorkshire faster than most people realise and they are genuinely loud in undergrowth at night.
That said if anyone's actually been out there with a decent audio recorder I'd love to hear what they've got. Even a phone recording would be something to work with. Has anyone tried setting up a trail cam? If this is happening regularly thats the obvious next step before jumping to conclusions.