Good Morning Britain presenter Morgan recently revealed that he had contacted police after receiving a series of death threats on Instagram.
Morgan, 55, shared screenshots of the threats, made in the comments of his and his 27-year-old son Spencer's Instagram accounts.
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Opening up about the situation in her Telegraph column, Walden, 45, said police had visited their home and that they had upped their security with a button that if pressed would bring officers to the door in four minutes.
She wrote: "It was only when I was told my phone number would be listed with a 'rapid response' unit specialising in death threats, and a security engineer came to install a panic button by our bed that would have the police there within four minutes, that a trembly feeling started up in my stomach."
Walden also voiced her concerns about having to explain the increased security to nine-year-old daughter Elise.
"I thought about the nine-year-old, I'd told to stay in her bedroom until 'Daddy's work colleagues have gone' and composed a convincing lie for when, as she inevitably did, my daughter asked what the contraption in our bedroom was for," she said.
The piece saw Walden call for an end to social media anonymity in an effort to limit such threats.
Last week, the unknown person left a comment on Spencer's Instagram account that included the words: "This isn't a threat, Piers it's a promise, you're getting killed."
Walden said Facebook, which owns Instagram, was helping police to track down the IP address of the individual.
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