Grosvenor was the youngest son of James and Mary Garnett (later spelling Garnet) née Withers
His father James was born in Newark in 1846 (J/A/S Newark) and his mother Mary Elizabeth Withers was born in 1851 (A/M/J Newark), also in Newark. They were married at St Mary Magdalene parish church, Newark, on 24 September 1871 (J/A/S Newark).
James and Mary had 12 children, all of whom were baptised at St Mary Magdelene, Newark: Florence Louisa b. 1872 (A/M/J Newark) bap. 11 April 1872, Lucy Kate b. 1873 (J/A/S Newark) bap. 21 August 1873, George Godfrey b. 1875 (J/A/S Newark) bap. 23 September 1875, William Percy birth registered 1878 (J/F/M Newark) bap. 7 March 1878, Harry Arthur birth registered 1880 (J/F/M Newark) bap. 16 March 1880, Ethel Maud birth registered 1882 (J/F/M Newark) bap. 8 January 1882, Margaret Annie birth registered 1884 (J/F/M Newark) bap. 27 January 1884, Conrad Stapleford birth registered 1886 (J/F/M Newark) bap. 10 January 1886), Violet Mabel b. 1887 (J/A/S Newark) bap. 31 July 1887, Olive Mary b. 1889 (A/M/J Newark) bap. 28 April 1889, James Barry b. 1890 (O/N/D Newark) bap. 12 October 1890) and Grosvenor birth registered 1894 (J/F/M Newark) bap. 28 January 1894. The birth and baptismal registrations of the nine older children have the surname Garnett but Garnet in the case of the three youngest. The family's address on the baptismal records was initially William Street, Newark, but by the time the three youngest children were baptised (1889-1894) the address was Kirk Gate, Newark.
By 1901, when Grosvenor was 7 years old, his parents were living at 6 Wellington Road, Newark. His father James (54) was a traveller in wines and spirits. Only seven of their 12 children were in the home on the night of the census: William (23) a malster's clerk, Harry (21) an engine fitter, and Conrad (14), Violet (13), Olive (12), James (10) and Grosvenor.
By 1910 Grosvenor had left home and emigrated to Canada. His parents were still living at 6 Wellington Road in 1911.
His eldest sister Florence Louise married Henry Graham and they had two sons, Henry (b. 17 February 1899) and Robert (b. 14 January 1902). She was widowed young and both sons died in the war, Henry in 1917 and Robert in 1918. (See 'Extra information' and their records on this Roll of Honour.)