Would the other children have been born in Liverpool? I had just found these:

SHAW WILLIAM : Service Number - 81058 : Date of birth - 14 Apr 1902 : Place of birth - BOLTON ENGLAND : Place of enlistment - PERTH : Next of Kin - SHAW JOSEPH
Series number
A9301 Control symbol
81058 Contents date range
1939 - 1948

Title
SHAW WALTER ARNOLD : Service Number - 88156 : Date of birth - 04 Jun 1923 : Place of birth - STAFFORD ENGLAND : Place of enlistment - HOBART : Next of Kin - SHAW JOSEPH
Series number
A9301 Control symbol
88156 Contents date range
1939 - 1948

Title
SHAW WALTER ARNOLD : Service Number - T29870 : Date of birth - 06 Apr 1923 : Place of birth - STAFFORD ENGLAND : Place of enlistment - DEVONPORT TAS : Next of Kin - SHAW JOSEPH
Series number
B884 Control symbol
T29870 Contents date range
1939 - 1948

No luck yet with Eric.

sue