A yellow non-statutory sign saying that "pedestrians do not have priority" does not imply anything remotely like a prohibition of pedestrians. It suggests an attitude by a landowner to pedestrians which is hardly in the spirit of the Highway Code, but it's not a prohibition.

It's not just my feeling about access tags. The second paragraph of the wiki page for access=* says "Access values describe legal permissions/restrictions and should follow ground truth; e.g., signage or legal ruling and not introduce guesswork. It does not describe common or typical use, even if signage is generally ignored."

There's currently a discussion of this in the Talk-GB mailing list, starting at https://lists.openstreetmap.org/pipermail/talk-gb/2024-March/031184.html