Here's a theory, but needs more research.
In 1910 he was found not guilty of a charge, named as Alan Morton, showman.
The record lists 4 other charges (some in the newspapers above) named as Allan Bosco, Allan Boscoe, Allen Boscow, Alan Boscow. Sharing link
If so, this could be them in the 1921 census (I haven't found them as Bosco in the 1921 census)
https://www.findmypast.co.uk/transcript?id=GBC/1921/RG15/18121/0355/07&expand=true 1921 census
: James Winrow Head M 28 Ormskirk, Lancashire, England Underground Wireman Telephones G P O Telephones
: Lillian Winrow Wife F 25 Southport, Lancashire, England Home Duties
: William Henry Winrow Son M 5 Southport, Lancashire, England
: Dorothy Winrow Daughter F 3 Southport, Lancashire, England
: Allen Morton Boarder M 39 Shipley, Yorkshire, England Motor Lorry Driver Own Account
: Florence Morton Boarder F 34 Islington, London, England Home Duties
: Joan Florence Morton Boarder F 0 Southport, Lancashire, England
Two possible births for the children on the 1939 census:
MORTON, ALLAN BIRCH
GRO Reference: 1920 J Quarter in CHESTERFIELD Volume 07B Page 1607
MORTON, JOAN FLORENCE BIRCH GRO Reference: 1921 J Quarter in ORMSKIRK Volume 08B Page 1737
Possible birth for Florence:
BIRCH, FLORENCE AMY -
GRO Reference: 1887 S Quarter in ISLINGTON Volume 01B Page 206
Still no marriage found.