It is hard to be safe to be honest - so you have to evaluate risk. A wind of 25mph can bring an old tree down because with 25mph comes gusts of up to three times that. Consequently, what may feel safe with branches swaying in the canopy can still be dangerous.
I am happy working in my wood at up to 25mph - higher than that and the gusting is unpredictable and in an ancient wood, anything can happen. That isn't to say I don't work in there above that but I wouldn't elect to camp in there if I had a choice. I actually like it when the trees are talking to me
- but I wouldn't take anyone else in to camp in those conditions.
The destruction capability of a large tree is astonishing and the ability of a broken branch stump, powered by several tons of trunk behind it, to pierce through stuff is frightening - they will go through steel and concrete structures. My point being, it is impossible to camp in a wood in high wind and be 'safe' - you may be able to reduce risk, lessen the impact, protect from the more likely, but you can't be 'safe'.
The worst scenarios are when the wind is blowing from an unusual direction. Our normal wind direction is westerly and the trees have grown surviving high winds from that direction. When we get Easterly storms we lose more trees.
Clearly, one can reduce risk by choosing a camp site that has no large trees (anything over 150mm trunk diameter can be dangerous), or hanging branches especially from the windward side. The strength of the wind can be considerably reduced on the leeward side of the wood but, strangely, that's where we get most of our wind blow.
Don't assume that a large trunk, previously fallen, will give you protection - it might, but another large tree falling on it may well make it collapse and, as mentioned above, piercing branches are as much of a danger as anything.
On one occasion, when I had little choice, I slept with my back against a large tree - I could feel no movement at the base and branches tend to fall away from the trunk - typically breaking off somewhere along the branch (not so with beech!). So, I figured, if things got so bad that the tree was likely to come down I'd have warning and be woken by the movement. Luckily, I didn't need to test my theory as I'm not sure it was sound logic