What it can actually constrain
Development. Planning policy gives substantial weight to protecting ancient woodland and the ground around it, which can affect applications for building on, near or with access across the land in question.
If you have plans — an extension towards that boundary, a new access, outbuildings — it is worth establishing where the designation runs and what buffer applies before you commit. If you have no plans, it will not reach you.
It can also work in your favour: a protected habitat beside a property is a strong constraint on anybody else building there, which is more than most buyers can say about the land next door.
The question that gets asked
Your conveyancer will ask the seller whether they are aware of any impact of the woodland on the property, which is the right question and often produces the whole answer — a tree preservation order, a management agreement, a right of way used by the public, or nothing at all.
Two things are worth adding to it. Whether any trees on the property itself are protected, which is a different and more common constraint. And whether anything in the title refers to the woodland — rights of access, obligations about fencing, or restrictions on use.
The local authority holds the records for both tree preservation orders and designations, and they are public.