Greenoak was founding horticultural director of the show from 1990.
In 1993, the RHS took over the running of the show, after Historic Royal Palaces accepted the society's bid on condition that it undertook to keep certain staff on the payroll, including Greenoak.
Lindsay Swan and Sylvia Holder of Holder Swan did the PR for Hampton Court Palace Flower Show from 1992 to 1999, starting while it was run by LeTeurnier-Boyd with Network Rail sponsorship and after that with the RHS.
They said: "Adrian was wonderful to work with, we had our best of all client relationships with him. He was receptive to ideas, always appreciative and if he believed in you, he would support you 100 per cent, as in the transition to the RHS: it was thanks to Adrian that we stayed on as PR consultants.
"Adrian was a polymath, an accomplished musician, composer, writer and academic. He was always entertaining company, a great conversationalist and loved talking into the small hours. He was generous too – when he left for Crete he gave a number of shares to the Venkat Trust, the charity Sylvia set up and now runs and the dividends still come in every year.
"He was wonderfully eccentric. I remember as the flower show came closer in our first year of working on it, we (and others) were surprised to discover that Adrian slept in the office, although being nocturnal I’m not sure he would do much sleeping. He had too many ideas/ too much music to play/books to write for that. One time when we were with him in a West End restaurant, he spotted a grand piano and proceeded to play one of his own compositions on it.
"Most of all he was a brilliant horticultural director. As well as his great horticultural knowledge and all his many friends and contacts in the industry, he had the clearest of visions for Hampton Court Palace Flower Show. To everyone else it was still just 25 acres of Home Park but Adrian knew what would work and went on to make it happen. After leaving the RHS, he went on to have success as the creative director of the Adelaide Rose Festival.
Former RHS shows director Stephen Bennett said: "He was innovative, passionate and a little eccentric, and introduced several innovations at the Hampton Court show which I supported and indeed introduced to other RHS shows e.g. the Plant Village concept and encouragement of more innovative floral marquee displays. Also the term 'show garden' was his (from the slightly less accurate 'garden')."
A RHS spokesperson said: "We were saddened to hear of the death of Adrian Greenoak. Adrian worked at the RHS for a number of years as director of horticulture for the RHS Hampton Court Palace Flower Show. His work helped set the foundation for what has become one of the world’s top gardening events."
His sister Francesca is a prolific writer and a previous gardening editor of The Times.