Richard Barry Parker was born in Chesterfield. His training covered furniture and textile design as well as architecture. In 1894 Parker opened a practice in Buxton, Derbyshire and in 1896 went into partnership with his half cousin Raymond Unwin. They designed houses in an Arts and Crafts style, and became interested in applying these principles to working class housing.
In 1904, they won the commission for laying out Letchworth Garden City. This was followed by the contract for Hampstead Garden Suburb in 1905, where they worked with Edwin Lutyens. The partnership ended in May 1914. Parker continued in both general and town-planning practice, working in the UK and overseas.
He died at Letchworth on 21 February 1947.