Right, so this is exactly the kind of thing that keeps me up at night - not in a good way either.
I've had similar out in the Pendle area. Something big moving through dense woodland, no visual, just this awful sense of scale from the sound alone. Snapping branches you'd need a decent sized animal to break, not a fox or a badger. The rhythm of the movement was wrong too - almost deliberate, like it was aware it was being listened to.
Few questions because details matter here:
What time roughly?, Any smell? People don't mention this enough but large cryptids allegedly carry a distinctive odour, Did it stop moving at any point, like it was listening back?, Any dogs in the area going mental or going completely silent? Both are significant apparently
I had my Olympus LS-22 out one night trying to get EVP recordings near the treeline and picked up something that still doesn't have an obvious explanation - heavy bipedal rhythm, slow, maybe 40-50 metres in. Never got a visual obviously because that's just how this stuff works isn't it, brilliant.
The Pendle woods have a long history of something and I've wasted enough weekends out there to know that conventional explanations run out pretty quickly once you're actually in it.
What county are you in? That context matters more than people realise. Some regions have much more consistent large cryptid activity than others.
Don't let anyone tell you it was definitely a deer. Deer don't make you feel watched.