I'll refer back to my post on the Beatles' "P.S. I Love You" from June of last year for some previous consideration of songs that blur distinctions between verse and chorus. While I had argued that the Beatles song might be considered to be all chorus, and that's clearly not the case with this song, "When Will I Be Loved" perhaps comes close and as such might be considered to be of a similar type. (A type that doesn't happen every day.)
To me, this case seems a little clearer. This song starts with the chorus, which is eight bars long. It then repeats the chorus with new words. That, in a nutshell is the trick; it's treating the chorus like a verse. When the chorus appears for the third time, it has new words yet again. That said, it's never treated otherwise like anything other than a chorus. The parts in between lead in to it absolutely and when you hear it for the fourth time, it just repeats the words.
The question is, what is that part in the middle ("When I meet a new girl" etc.)? It certainly sounds to me like a bridge that's repeated once. I can't see anyone calling it the verse.
So, we have here a song with four choruses, two bridges, and no verses.