Anthony's parents were George Gibson, a mason, and Elizabeth Goodman who were married in 1848 at Sprotborough. They appear in the 1851 census in Mexborough with one child, Arthur J who was one year old. When Anthony was born in 1857, George was listed as a stone quarryman. By 1883 he was titled as a labourer. The family were living in Hall Gate, Mexborough in 1881 - George and Elizabeth, and sons Arthur J, Anthony and Walter. Arthur had followed his father to the stone quarry, and Anthony was a bottle maker. There were hundreds employed in glass works in Mexborough at the time, including that of Thomas Barron which was set up by the River Don in 1850.
Clara's parents were Alfred Barber, a railway platelayer and Dinah Shallcross. They had been married in 1858 in Attercliffe. She was the second child of five, with brothers Fredrick, Dyson and Clevin, and sister Tiley. Clara was born on 26 August 1862 At Gallow Trees, Wath-on-Dearne. By about 1873 the family had moved to Mexborough, and in 1881 their address there was Dolcliffe Cottage.
On 28 February 1883, Clara Barber married Anthony Gibson, a glassblower of Mexborough at Spring Gardens Primitive Methodist Chapel in Doncaster. The chapel, the second to have been built in Spring Gardens, was opened in October 1854, having been designed by William Sissons of Hull. By the time that son George Alfred was born in 1889, Anthony and Clara were living at 20 Doncaster Road, Mexborough. Anthony was then described as a glass bottle maker. There were five other children: Frank, Edith, Dinah, Henry and Arthur.