In each book I have there is only Anzani Cyclecar, 1098cc, 1923-1924 except the Beaulieu:
Anzani: See Mauve (F)
Mauve:
Eugène Mauve built nad raced the Elfe cyclecar from 1919 to 1921, and the following year turned to a more conventional car powered by a 1086cc single-ohc 4-cylinder anzani engine. He raced the first under the Anzani or Mauve-Anzani, which as led to Anzani being listed as a make of car. Production cars, however, were always called Mauve...(...).
but in the "New Encyclopedia":
ANZANI (I) 1923-1924
Motocicli e motori Anzani, Milan
(....) A factory was opened in France, and Anzani engines were also made in England by the British Anzani Company.(....)
Alessandro Anzani himself settled in France, near Caen, and altough no car appeared after 1924, proprietary engines bearing the name were produced until the 1930s, and after WWII in England.
I don't know why there is nothing about Alessandro Anzani in the Beaulieu, but I have listed this car as an Anzani Cyclecar...and other sources reported his activity in Italy, France and England as engine supplier (England) and builder of cyclecars (Italy) and light 2-cylinder cyclecars (France).
Finally I have a good picture of this Anzani Special!