Inspector Terry Clawson said: "The page has since been taken down but has already caused unbearable upset for Kiri-Jade's family and friends.
"We're taking this matter very seriously and investigating it from a criminal perspective.
"We're working with Facebook and following other lines of inquiries and we will be taking appropriate action.
"If you have any information that can assist with our inquiries, please contact us directly. If you come across any similar sites, please also let us know and avoid commenting on them."
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Sir Bruce entertained audiences for more than seven decades.