Union Unite has said the RHS is "flatly refusing" to talk to unions over its "Change Programme", which is seeking a 10 per cent cut in the salary bill.
But an RHS representative has said Unite has no mandate to represent its staff and is "misrepresenting" the organisation's handling of the redundancies.
Unite national secretary Chris Kaufman said "low-paid" gardening staff are most at risk from cuts and "horticulture standards would then decline".
"Why is it that gardeners on around £16,000 face job cuts and the loss of their pensions and possibly their homes, yet the charity expands its very highly paid management team?" he asked.
"This is surely not in keeping with the public image of an organisation of the stature of the RHS."
Kaufman would not reveal how many RHS staff are union members but said 40 had unanimously voted "no confidence" in the consultation procedure last week.
He said RHS "intransigence" meant "we have to enage the public to stop this being bulldozed through".
RHS communications director Lynn Beddoe replied: "Unite has no mandate to represent RHS staff, and we have therefore declined the union's request for a meeting.
"We are in discussions with the RHS employee consultation group (ECG), which is elected by staff, about the proposed changes.
"We have agreed with the ECG that the process is best handled through a single, elected body which is representative of all RHS staff, and which shares detailed understanding of our diverse activities and operations.
"Unite is misrepresenting both the circumstances of the RHS and the detailed process of consultation, which is now entering its third month."