Wedgwood was born in Etruria Hall, the son of Francis Wedgwood and his wife Frances Mosley. He was taken into partnership by his father in 1859, and was later joined by his younger brothers Clement and Laurence. He and his brothers were responsible for the reintroduction of bone china c. 1876 and the employment of the artists Thomas Allen and Emile Lessore.
He married twice, first to Mary Jane Jackson Hawkshaw (c. 1836-1863) on 24 June 1862 at St. Peter Pimlico, Westminster, Middlesex with whom he had a son Cecil Wedgwood (1863-1916); but she died in 1863 due to complications of the birth of Cecil. And secondly on 14 October 1876 in Marylebone Register Office to his cousin Hope Elizabeth Wedgwood, daughter of Hensleigh Wedgwood. They leased Caverswall Castle in Staffordshire between 1878 and 1888. They had a daughter Mary Euphrasia Wedgwood (1880-1952). Godfrey Wedgwood died at Idlerocks and is buried All Saints Churchyard in Moddershall, Staffordshire.
- Obituary The Times, Thursday, Oct 12, 1905; pg. 4; Issue 37836; col A