The High Court heard how the newspaper had said that the father, known only as KC, was convicted of raping a 14-year-old girl.
Publisher MGN Ltd had apologised and previously offered to pay damages, but the judge said today that it was "difficult to think of any charge more calculated to lead to the revulsion and condemnation of a person's fellow citizens than the rape of a 14-year-old girl".
At an earlier hearing, James Dingemans QC, representing KC, told Justice Bean that the publisher's offer of damages came too late and was not enough compensate the father for "one of the gravest libels imaginable".
The false allegations were published on September 19, 2010, as part of a crime supplement about Baby Peter's mother Tracey Connelly, who had separated from KC.
Connelly was imprisoned in 2009 after admitting to causing or allowing the death of the 17-month-old infant in Tottenham, north London, in August 2007.
She was jailed alongside her boyfriend Steven Barker and their lodger Jason Owens after Baby P was found dead with more than 50 injuries.
Dingemans said that The People's allegations about Baby P's natural father in the wake of the killing were "shocking and appalling". He also said that publisher MGN had treated KC "as if he didn't really matter".
Heather Rogers QC, representing MGN, said: "This was a mistake that MGN regrets and it has apologised to the claimant, and I repeat that apology on its behalf in this court."
Justice Bean said that the nature of the accusations against KC were "far worse" than in other similar cases, and so MGN should meet his demands for a £75,000 settlement.
After Rogers requested an appeal on the grounds that the compensation was "disproportionate", the judge refused the request, but placed a stay on the damages element of the settlement at £45,000 until the Court of Appeal decides whether to hear MGN's case.
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