Frank was the son of George and Annie Wagstaff.
George and Annie (née Smith) were married in Nottingham in 1874 and had at least seven children: Annie b. Nottingham 1875, Henry/Harry b. Nottingham 1876, Walter b. Chapeltown Yorkshire 1878 d. 1898, Frederick William b. Carrington 1881, Charles Matthew b. Carrington 1883, Clara b. Radford 1887 and Frank b. Radford 1889.
Frank's sister, Annie, was identified from a list of Frank's living relatives which his married sister, Clara Wood, completed for the Army in 1919. Clara named a married sister, Annie Faulkner (45), who lived in Shirebrook. Annie was not recorded in the family home on any of the census between 1881 and 1901 and it is likely that she is the Annie Wagstaff who at the time of the 1881 and 1891 census was living with her grandparents, Matthew and Mary Wagstaff, in Chapeltown, Ecclesfield, Yorkshire. Annie Wagstaff married Cornelius Faulkner in Nottingham in 1898 and in 1901 they were living in Killamarsh, Derbyshire, with their son, Charles (2). By 1919 they were living in Shirebrook.
In 1881 George, a bobbin and carriage maker, and Annie were living at 11 Rose Yard, Bridlesmith Gate, Nottingham, with their two sons, Henry and Walter. By 1891 they were living at 43 Ossington Street, Radford, with their six youngest children, Harry, Walter, Fred, Charles, Clara and Frank (1). In 1901 the family was living at 26 Beaconsfield Street, Radford; only the three youngest children were in the home on the night of the census; Charles, Clara and Frank.
Frank's brother, Walter, probably died in 1898 aged 20. His father George Wagstaff died on 15 October 1903 aged 47 and his mother, Annie, in 1904 aged 47.
Frank joined the Army in 1906.
Frank's sister, Clara, married Charles Henry Wood, a lace maker, in 1908. In 1911 they were living at 50 Lyndhurst Road, Sneinton Dale; they had had one child who had died. Visiting them on the night of the census was Clara's niece, Annie Elizabeth Wagstaff (4).
Frank's brother, Charles, who was a steel hardener for a telephone manufacturer, was also married by 1911. He and his wife of five years, Minnie, and their children George, Charles Leonard and Hilda Clara, were living at 23 Trafalgar Road, Beeston.
Details of Frank's living relatives from information provided by his sister, Clara, in 1919: Brothers, Harry Wagstaff (44), 45 Maples Street, Nottingham; Charles Wagstaff (35), 23 Trafalgar Road, Beeston; Fred Wagstaff (39), 12 Ireton Cottages, (-) Street, Nottingham. Sisters, Annie Faulkner (45), 78 Market Street, Shirebrook; Clara Wood (33), 278 Alfreton Road, Nottingham.