William Frederick was the son of Henry and Rebecca Greasley (née Brownley).
Both his parents were born in Nottingham, his father in about 1863 and his mother in about 1864. Henry and Rebecca were married at Sneinton St Matthias in October 1883 and had eight children, three of whom died in childhood: Sarah Beatrice b. 1886 and John Thomas b. 1888, both baptised Nottingham St Ann's 1889, Henry b. 1891, Elizabeth Hannah b. 1893 d. 1894, William Frederick birth registered 1897 (J/F/M), Alice EM b. 1901 d. 1904 (O/N/D), Rebecca Florence b. 1902 d. 1904 (O/N/D) and Bernard Edwart b. 1906.
In 1889, when Sarah and John were baptised, the family was living at 19 Beverley Street, Nottingham, but by 1891 had moved to 5 Agnes Terrace, Dame Agnes Street, Nottingham, where they were still living in 1911.
In 1911 all five children were still living at home with Henry, a printer, and Rebecca: Sarah (26) a barmaid, John (23) a warehouseman who was married, Henry (21) a fitter cycling, William (15) a butcher and Bernard (4). Their second son, John, had married Sarah Ann Murphy in 1906 and they had a daugther, Lilian Beatrice, the following year; In 1911 they were living with her widowed mother, Mary Ann Murphy, on Beverley Street.
The later CWGC record gave William's parents' address as 80 Beverley Street, Nottingham, and Henry and Rebecca were still at the same address in 1939 when the England & Wales Register was compiled. Also in the household was their son, Bernard.
Henry died the following year in May 1940 and Rebecca in December 1943.