Richard Madeley and Judy Finnigan have confirmed they have made a formal complaint to the police after online rape threats were made against their daughter Chloe.
The family said they have handed over "a substantial amount of evidence" to the police.
The 27-year-old was the target of online trolls after she defended comments made by Judy during a debate around the future of rapist Ched Evans, in which her mother said his crime was "non violent" and did not cause "bodily harm".
A statement from the family said: "Following legal advice, our family has now made a formal complaint to the Metropolitan Police about cyber-stalking, harassment and, most recently, rape threats made against Chloe on Twitter.
"We have presented the police with a substantial amount of evidence, and they have launched an immediate investigation.
"We will be making no further comment at this time."
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article