Gated road in a country park

There is an unsurfaced road in a country park near me, with locked gates at either end. It’s available to the public as a footpath. It’s currently tagged as highway=unclassified, with 2 highway=gate nodes.

http://www.openstreetmap.org/?lat=51.49212&lon=-0.34811&zoom=16&layers=B00FT

It shows on Mapnik as a through road, so I was going to add access=private, but that would suggest you can’t walk on it. Does the current tagging work (meaning it’s a rendering issue) or is there some other way to tag this correctly?

Thanks

Oliver

Perhaps highway=track is more appropriate than highway=unclassified. Presumably the road is owned and operated by the country park and isn’t part of the wider highway system.
highway=track with either foot=yes or foot=permissive.

Or you could use leave it as it is and add motorcar=no.