A native of Mansfield, Nottinghamshire, Wright Barker later went to live in Newark and in 1903 moved to London, settling in Hampstead.

However, it was his Nottinghamshire background, which inspired his work throughout his career. He painted the local hunts and woodland areas, the people who lived there and the events, which made up their annual calendar, such as the visiting fairs and sporting events. He had a great love of animals and occasionally painted portraits of domestic pets, sometimes with their owners.

He exhibited at the Royal Academy, fourteen paintings in all between the years 1891 and 1904 and he also exhibited once at Suffolk Street.

His works can be found in public collections including Bradford Museums and Galleries; the Mercer Art Gallery, Harrogate; Ferens Art Gallery, Hull; Kirklees Museums and Galleries.