The news emerged at a meeting where he answered questions from local residents about the future of Royal Botanic Garden Kew.
Deverell said just one redundancy notice had been served so far, adding that other redundancies - 125 posts are expected to go - had come from job vacancies not being filled and two rounds of voluntary redundancies.
He said his best guess was 10-12 per cent of science jobs could go.
Deverell added that Kew is considering charging children for the first time, "a contentious issue", but could reduce costs for students and the unemployed, as well as cutting the entry from £15 to £9.50 in winter.
Family tickets could cost no more than two adult tickets. He said there was visitor resistance to the £15 entrance fee rising.
Deverell said Kew would go bankrupt if cuts were not made urgently. He said a funding shortfall of £5.5m meant a hole in the operating budget.
Union Prospect has called for Kew to delay cutting 42 posts until after the select committee meeting but Deverell said he did not want to delay because of the risk of bankruptcy and because Kew staff wanted the process to be over.
He said by December 1 all science redundancies would be completed.
A new science strategy will be written by January 2015.
See more in the next edition of Horticulture Week magazine.