Chris Mills, head of library, art and archives, said the gardens were half funded by Defra and across-the-board cuts expected in the spending review were a worry.
He spoke on the official opening of the £19.3m herbarium, an event supposed to be attended by environment secretary Caroline Spelman who dropped out at the last minute prompting speculation of bad news.
Mills said: "We have never been lavishly funded and we have some control. We generate our own resources through gate money and scientific consultancy. But our work on climate change is crucial.
"It's a concern and some things may have to go on hold. This concern is especially the case with something like this new facility coming on stream. We don't want to have to cut back on what it could allow us to do."
The herbarium includes study areas, a library, cold storage and archive for eight-million specimen plants wrapped up in modern curvaceous elevations of western red cedar, pale bronze and red brick.