There are 8 Gregory children born England / Wales 1890-1912, mmn Mellers. Registrations are in Wortley and Sheffield. The first 1894 and the last 1907.
The parents’ marriage is probably this one:
John Gregory & Annie Elizabeth Mellers, Sheffield, March quarter 1894.
A matching family is at 91 Bolsover Road in 1911. Married 17 years.
This all supports barry’s pick of the Gregory-Cocker couple.