Detectives are in talks with prosecutors after investigating reports that Peaches Geldof named the two mothers whose babies were involved in abuse by disgraced rock star Ian Watkins.
The daughter of Boomtown Rats star Bob Geldof posted the names of the two women on Twitter, the internet social networking site, after reportedly reading them on an American-based website - but has since removed them.
Lostprophets singer Watkins was branded a "determined and committed paedophile" after he pleaded guilty on Tuesday to a string of sex offences, including the attempted rape of a baby.
The 36-year-old, from Pontypridd, Wales, plotted the abuse with the two mothers in a series of text and internet messages.
Senior investigating officer Detective Chief Inspector Peter Doyle, of South Wales Police, said: "We are aware that the names of Ian Watkins' co-defendants have been published on social media channels.
"Clearly, there is strong public feeling about this case and many people are using social media forums to talk about the issues involved.
"We are in consultation with the Crown Prosecution Service regarding the matter and will take action if appropriate.
"Our primary objective as an organisation remains the safeguarding of vulnerable people and children.
"Victims of sexual abuse have a right to anonymity to protect their future welfare and we urge those discussing the issues raised online to be careful about using information that identifies victims in cases like this."
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