In 1949, he joined the first committee for the Northern Horticultural Society's new botanical garden, Harlow Carr, which opened to the public in 1950. He later served as president of Harrogate Flower Show and the Northern Horticultural Society.
Compton and his wife, Janey, restored the gardens of his home in Yorkshire, Newby Hall, establishing a national collection of Cornus. He was awarded the Christies-Historic Houses Association's Garden of the Year award in 1988 and the RHS Victorian Medal of Honour in 1994.
Plant Heritage executive officer Genevieve Melbourne Webb said: "Robin was a passionate supporter and he maintained a very close interest in the charity's work."
There will be a memorial service at 2.30pm on 3 February 2010 at Ripon Cathedral.