The Jewish owner of The Ivy restaurant is offering £15,000 reward for capturing the vandal who shot two stags on his estate.
Police are investigating the possibility that the attacks may have been intended to send a threatening message to Mr Caring.
Richard Caring, who also owns celebrity hotspot Annabel’s nightclub, has now hired former SAS soldiers as security guards for his estate in Exmoor.
The businessman, who is 146th on the Sunday Times Rich List and worth an estimated £360 million, called the hunter “a lunatic with a high-powered rifle”.