There is a great database of openstreetmap errors on https://www.keepright.at/ and I built a little web tool on top of it to quickly go through the errors. It is super addictive and I currently try to release it to the public. Send me a PM if you like to try it out - it isn't public-ready yet because you need to understand what happens to not mess up the road network ;-)

Oh yes, the information is really vague. This will make it a bit difficult to conclude routing rules from it that are correct worldwide, not only in UK.
Let's see if that is possible and if there are any conflicts popping up.
Thanks for your summary, this helped me a lot to understand the issue here! Best, Jan

Hey mike, thanks for the explanation! I was looking for a reference of your statement "The designation=public_bridleway would set the default access of foot, bicycle and horse=yes" but I couldn't find it in the wiki, I really would like to implement it correctly in our routing, Can you give me a reference? Thanks in advance!

Dear Mike, Looking at the wiki, one should indeed make the usage clear with appropriate access tagging:

"Also taginfo shows a significant number of uses of:
designation=permissive_footpath
designation=permissive_bridleway
These tags should be used in combination with an appropriate highway=* tag, and appropriate access=* tags."
osm.wiki/Key:designation

I think that bettyA did it correctly. What do you think?