I’m seeing similar with these type of roads in Suffolk. I believe the solution may be to set the expressway=yes tag on OSM.
Based on the definitions of an expressway on OSM it looks perfectly valid for the A308 (name=Staines By-Pass). Looking at the Overpass Turbo query it appears these expressway=yes nodes will be filtered out.
I think this will solve quite a few cases in the UK that are technically legal to access on foot, but are not remotely safe or sensible to run along.