It is possible that William Arthur's father was Robert Alfred, he was born in Cowley 1885 but birth registered in Uxbridge (the Cowley connection) he died in 1934 his wife Phyllis died in 1952. The query ! they married in 1910 one year after William Arthur was born. There have registered the birth of 6 children to an Enever whose maiden name was Barlow. Cyril born 1912, died 1933, Ivy born 1913 died 1914, Ronald born 1914 married 1942 to Weeks and had two sons Robert 1944 & Walter 1945, Ernest born 1919, Alfred born 1920 died 1920 and Margaret born 1921, married Rogers in 1943.
If you look up the GRO marriage indexes for 1910 April-June for the name Barlow you should find a reference for Phyllis of vol 3A and page 80 if this is the correct person.