Probably the british Putin has disappeared. However it existed in Britain since I have found it in the site:
www.familysearch.org (Mormons'site).
I am sure that this surname exists in Italy: see
www.gens.labo.net and in France: LA FRANCE DE VOTRE NOM DE FAMILLE.
The italian variant comes from the VENICE region. Probably it comes from a dialect word "putin", that means little baby.