Piccaver was chairman of specialist producer JE Piccaver & Co and led numerous industry bodies and crop associations throughout his career, including the British Leafy Salads Association (BLSA), which he chaired from 2004 to 2009. In April last year, he became chairman of the Potato Council.
Graham Ward, chief executive of Stockbridge Technology Centre (STC), where Piccaver was a board member, described him as a "giant" in the industry whose growing and marketing skills "gave him the authority to talk from strength".
Ward added: "David's major contribution and passion was the importance of science for our industry. He championed R&D wherever he was. He joined the STC Board in 2009 and helped us considerably.
"I have lost a friend, STC has lost a director and the industry has lost a champion. We all owe a massive debt to David, and his family, for his outstanding contribution for our horticultural industry."
BLSA chair Colin Bloomfield said: "David was the person I noticed at the first BLSA meeting I attended. He had a distinctive voice that commanded attention, you knew you wanted to hear, an opinion worthy of your time, an opinion to mull over."
He added: "His role of science and the importance it must play in horticulture was striking. He had the enthusiasm of a newly qualified graduate, not what you might expect of a long-time practical Lincolnshire farmer.
"It was this importance of science that he took into his recent role of chairmanship of the Potato Council. It was his view that horticulture needed a distinctive voice that resulted in the expansion of the British Growers role to become that voice.
"All members felt his support and personal attention. If you left a message on the answerphone, you knew it would be answered."
Bloomfield said the BLSA prospered under Piccaver's chairmanship, which included undertaking a public relations role that evolved later under John Allan into the promotional campaign "Make More of Salads".
Colleagues at the Potato Council and AHDB said Piccaver's "passion for getting the right information to the right people" had left its impression on all of the potato sector.
"In the 1990s and 2000s, as chair of the R&D committee his desire to mix technology with people led to the 'Fight Against Blight', aphid monitoring and the first genuine real-time reporting of R&D through online reference crops and blight product tests.
"More recently, as an AHDB board member and chairman of the Potato Council, he returned with a clear business focus and a 'going for growth' attitude that was an inspiring and invigorating challenge for the staff, the board and the subcommittees of the Potato Council.
"He always said you should leave a place in better shape than when you found it and can rest in the knowledge that that's exactly what he did."