The future location of the National Fruit Collections has been brought into question because of problems between the current manager and landowner.
The 150-acre farm at Brogdale has about 50,000 visitors a year
Tenders are being taken for a contract to run the collections, currently at Brogdale, near Faversham, Kent.
But Brogdale Horticultural Trust said that if it kept the contract, a dispute with the landowner could force it to move from that site.
Hillreed Land said it was committed to keeping the collections where they are.
The horticultural trust's chief executive, Jane Garrett, said: "We would love to stay where we are.
"But we are unable to continue running our shop, tearooms and plant centre [at Brogdale], which are key parts of our income stream and fund other work we do with the public around the country."
Ms Garrett said this was because the trust's commercial arm had "not been invited to come back" when Hillreed Land completes a £1m refurbishment project at Brogdale.
But Hillreed's chairman, Tony Hillier, argued the trust had been "too late in telling me they wanted to extend those opportunities, and I had to make other arrangements to keep that offer on site".
Mr Hillier said the trust's lease at Brogdale had therefore only been extended in terms of maintaining the fruit collections during the tendering process.
He added that Hillreed's commitment was to see Brogdale "retained as the home of the collections".
The living "gene bank" of fruit types - including apples, pears, plums and cherries - has been at the farm for more than 50 years, with the horticultural trust managing it for nearly two decades.
But a clause in the government's tender document says: "Bids can, if appropriate, also include plans for relocating the collections."