Eyton was born at Eyton Hall, near Wellington, Shropshire. He studied at Cambridge University with his friend Charles Darwin. After succeeding to the estate in 1855 Eyton built a large natural history museum at Eyton Hall.
Eyton published History of the Rarer British Birds (1836), A Monograph on the Anatidae, Or Duck Tribe (1838), A History of Oyster and Oyster Fisheries (1858) and Osteologia Avium (1871-78).
He was born in Glasgow, the eighth son of Alexander Campbell, His father, of the family of Campbell of Kirnan, Argyll, belonged to a Glasgow firm trading in Virginia, and lost his money in consequence of the American Civil War.
Campbell was educated at the grammar school and university of his native town.
Thomas J. Campbell (1927-) was a Mayor of Vancouver from 1967 to 1972.