If you want to explicitly specify a footpath, highway=footway already does that.

It doesn't do any harm to add the extra access tags, but you don't generally need to add horse=no or bicycle=no, or any of the other irrelevant options which the iD editor presents for footways (I wish it didn't). It can be worth adding bicycle=no where it is explicitly signed, but still isn't absolutely necessary. 

The OSM wiki lists the UK's default access restrictions for different highway types here.
https://wiki.openstreetmap.org/wiki/OSM_tags_for_routing/Access_restrictions#United_Kingdom