No relation whatsoever, rather an example of a major part of British paper based entertainment - the story paper. This "Adventure" started in 1921. Many others existed at one time or another, Wizard; Hotspur; Girls' Crystal; Schoolfriend; Ranger; Scoops and on and on. They contained illustrated prose stories and as time went on, the odd comic strip, or rather text strip as opposed to balloon strip, was introduced. The closest to an American crime/gangster pulp was The Thriller, a weekly paper with excellent, atmospheric illustrations and fast paced storylines. The Saint and The Shadow appeared in its pages.
Logos did change over time but I've no idea if this one was influenced by the American one. Can anyone else help?