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Garden collections supervisor Barbara Wheeler said the camera would be put in place this week after vandals damaged the recently installed worm sculpture Ouroboros at the weekend.
The camera had been used in the gardens before when issues had cropped up, she said.
Information from it would also be used to determine what times security guards should do their rounds of the garden, which was locked at night.
The garden team would start discussing plans for CCTV next week, including when it would be installed, what areas it would cover and how it would be monitored.
Installing CCTV was ''a costly exercise'' so there had to be careful consideration before it went in, Ms Wheeler said.
There was a webcam centred on the central part of the garden, but it was a simple live-feed set-up that had no capacity for recording, she said.