Is there really an explicitly signed pedestrian prohibition on w1156071336? If not, then there isn't a pedestrian prohibition.

I don't believe that there are any circumstances in which the Street Complete "are pedestrians prohibited" quest will ever result in good tagging in Greater London. Either it adds an explicit and technically correct foot=yes (but giving unhelpful hints to pedestrian routers) or a fictitious foot=no. All of London's real pedestrian prohibitions through tunnels, over flyovers and on motorway-style roads have been tagged for years.