Honest caveat: this isn't a wander-anywhere wood. The ancient core is off-limits by design, so what you're actually walking is the footpath network around and alongside it — still a lovely stretch of the Avon valley, and easily combined with the Avoncliff Aqueduct and Cross Guns pub, but don't come expecting free rein through the trees.
Thirty hectares of ancient woodland and adjoining fields between Freshford and Avoncliff, taken on by the Woodland Trust in 2019. Be aware the wooded core itself is run as a closed conservation area — a 'living laboratory' left largely undisturbed — but public footpaths cross the surrounding fields and skirt the wood on the way between the two villages, with kissing gates marking the route.
Woodland Trust wood — free to visit on foot, open every day.