I'm not making any of this up, it's years of established best practice. https://wiki.openstreetmap.org/wiki/Further_guidance_on_tagging_Public_Rights_of_Way_in_the_United_Kingdom#Access_conditions

"

When adding access=* tags to a highway that is also a PRoW you should only add the tags granted to that highway by the PRoW status – unless other legal access restrictions are verifiably known. In our public footpath and service road example, the following is correct if we know nothing else about any other legal access restrictions on the road:

    highway=service
    foot=designated (this is the only access tag we are certain of)
    designation=public_footpath
    prow_ref=*

You should not assume that access is, or is not, permitted by other transport modes. It may not even be possible to determine this from a ground survey.

Although the legal access may not be explicitly covered by the PRoW type, other transport modes may still be allowed. For example, cyclists may still be allowed on a public footpath."