In the 1921 census his birth place is Huddersfield, birth year 1883, age 37y 10m. I looked at 2 other possibilities - at Beech Cottage, Trafford Rd, Eccles and 43 Church Lane, Gorton but the birth places didn't fit.
His dob on the GRO certificate is 10 Aug 1882, father James Henry, Mother Mary Ann formerly Jebson at Hill Top Paddock Huddersfield.
The only listing in the 1939 register whose birth date matches is for William E. Shaw, married, Traveller Salesman, with Lilian M. Shaw married, born 14 May 1889, domestic duties. Both at 160 Liverpool Rd, Huyton with Roby.
His death certificate says he died 21 Feb 1952, age 60, at County Hospital, Whiston of bronchial pneumonia. His address is 160 Lpl Rd, informant L.M. Shaw, widow of same address. The only rather dubious point is his given occupation - formerly motor engineer and mechanic.
I will look for a possible bigamous marriage but it's more likely they were just living together.
Thanks to all for their helpful suggestions.