Broadcaster Vanessa Feltz has been allocated extra security after she received threatening emails including one in which she was told she would be beheaded.
The 54-year-old, who hosts two BBC radio shows, was targeted with a series of messages to her work account.
The mother-of-two, who presents on Radio 2 and Radio London, was said to have been left "shaken" and looking "stressed".
On Monday the Sun reported a source saying: "Any form of death threat is frightening for the target, but the threats made to Vanessa were especially vile.
"One even threatened to behead her. They were in emails and were taken very seriously from the start.
"It has been very difficult for her to cope with, and she is shaken."
A source close to Ms Feltz told the JC she had been advised by police not to comment on the episode.
It is not the first time she has been on the receiving end of abuse.
In 2014 she was inundated with online abuse after she told BBC radio listeners that Rolf Harris had assaulted her during a recording of Channel Four's The Big Breakfast in 1996.
She said Harris put his hand up her dress and felt her leg during an interview.
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