Interesting, in Ireland we don't have the red and white pedestrian sign, but we do have the likes of this[0] red and white taxi sign signifying a taxi rank (implicitly disallowing parking for non-taxis).

For "no pedestrians", we have what to my eyes much more sensible: the same sign as the Italian one but with a strike through it [1]

[0]http://st2.depositphotos.com/7458252/11066/i/950/depositphot...

[1]http://www.gettyimages.es/detail/foto/no-pedestrians-in-irel...