Blakely Rinder Gribbon was born in Melbourne, Victoria, Australia on 24 April 1884. Following the death of his father the following year he moved with his family to England. After his mother died in 1886 and he went to live with grandparents in Yorkshire. He subsequently practised as an architect in Yorkshire, however, it is not known where he trained. In c.1922 he joined Harry Sutton Chorley (1869-1939) in partnership in as Chorley & Gribbon. They had an office a 3 Park Place, Leeds. In c,1925 George Herbert Foggitt (1887-1975) joined the practice when it was renamed Chorley, Gribbon & Foggitt. They remained in partnership until at least 1939 when Chorley died.
Gribbon was elected an Associate of the Royal Institute of British Architects (ARIBA) in 1915, and a Fellow of the Royal Institute of British Architects (FRIBA) in 1929. He was awarded the Architecture Bronze Medal for West Yorkshire in 1931.
His address was given as Windsor Terrace, Garforth, near Leeds in 1915; 3 Park Place, Leeds in 1923 and 1939. He died in Ilkley, Yorkshire. He died on 13 December 1944