Giving us the name of at least your great grandfather would help in checking his whereabouts.
Plus, his age and occupation/s on 1921 census and 1939 Register. Also, names of his father and sisters.
Have you looked for him or his family on 1911 census?
You can ask on the military board if you want details or explanations of his service. There's a World War 1 section. If his records survive, they may include name/s & addresses of his next-of-kin. Did his discharge papers have address of his intended residence?
John Edward Schofield was born 1892 to Francis William Schofield and Lavinia Atkinson. He had siblings Edith, Lister, Annie, Ada, Bertha, Elsie and Hilda. So far I have only found that of his siblings only Edith, Bertha and Elsie were married and only Edith and Elsie had children. I managed to find a descendent of both Edith and Elsie but they don't seem to know anything.
In the 1911 census, he was still living at home with his mother and her second husband, (his father died in 1905 in a work accident) and his sisters Ada, Bertha, Elsie and Hilda.
On the 1921 census, my great grandfather John Edward Schofield age 28 was living with his sister Edith Norton (nee Schofield) and her husband and children in Wakefield. He was a "machine minder" in Dewsbury.
In the 1939 register he was living with his sister Bertha Dransfield (nee Schofield) and her husband Clifford, in Wakefield. They had no children as far as I can tell.
The service records I found online were just about his war pension. His own I think was for 1921 and it was the address where he was living with his sister Edith, there's a secondary address which I think is where he lived with his parents.