The natural father of Baby P is suing the publishers of a Sunday newspaper for £130,000 damages for printing "one of the gravest libels imaginable".
A judge was told the father, who cannot be named for legal reasons, was wrongly accused in The People of being a sex offender convicted of raping a 14-year-old girl.
The newspaper's publishers, MGN Ltd, later apologised and offered to pay damages.
However the offer came late and was not enough to compensate the father, referred to as "KC", for the suffering and distress the "completely false" reports had caused, said his QC James Dingemans.
The allegations were contained in two paragraphs in a crime supplement about Baby P's mother, who had separated from KC.
They appeared in The People on September 19 2010 in an article entitled "Tortured to death as mum turned a blind eye".
Baby P, later named as Peter Connelly, was just 17 months old when he was found in a blood-splattered cot at his mother's home in Tottenham, north London, in August 2007. He had more than 50 injuries.
Tracey Connelly was jailed in 2009 after admitting causing or allowing his death.
Her boyfriend Steven Barker and their lodger, Jason Owens, who was Barker's brother, were found guilty at the Old Bailey of the same charge.
Mr Dingemans said the allegations about the natural father in the wake of the Baby P tragedy were "shocking and appalling".
However MGN treated him "as if he didn't really matter".
Heather Rogers QC, appearing for MGN, told the High Court: "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."
However she denied KC had been badly treated, or that MGN had conducted any kind of "campaign" against him, or dismissed his legitimate complaint.
KC himself said in a statement before the court: "I was shocked and upset beyond words. I thought that the whole world would think that I was a really awful man.
"I could not believe that such an appalling, untrue statement had been published about me to the whole country,
"I feel that the defendant's whole approach has been to pretend I do not exist, because they did not contact me about the story, to treat me and correspondence on my behalf as an annoyance as not worth their time, and to belittle me and my feelings."
Mr Dingemans said of KC: "He is a man of good character, with no previous convictions living with the fall-out (of Baby P's death) day-by-day, and never a sex offender - never guilty of rape."
The rape conviction had been imposed on Baby P's maternal grandfather, the QC told Mr Justice Bean.
The first offending paragraph in The People article read: "At just 16 she [Tracey Connelly] met the father of Peter - 17 years her senior - and the two were married in Haringey Civic Centre. Her new husband was a sex offender".
The second, further down in the story, read: "Peter's real father had also reappeared and had begun making frequent visits - something that would have set off alarm bells at social services as he had been convicted in the 1970s in Leicester for raping a 14-year-old girl.
The inaccurate reports appeared in the middle of care proceedings relating to KC's other children and, as a result, he was put in fear of losing them, said Mr Dingemans.
He added: "It is not sustainable to try and suggest this was a narrow publication."
The newspaper had a circulation of about 500,000 and a readership of about 1.2m persons throughout the UK.
The QC said: "This was a publication to the whole world that the father of Baby P was a sex offender and rapist. They were the gravest allegations one could possibly make."
An appropriate award was the sum of £130,000, Mr Dingemans told the judge.
Mr Dingemans said at the time the rape allegations appeared, the family court proceedings in relation to KC's other children were ongoing and it was "one of the most pressurised times" of his life.
The court-appointed guardian looking after the children's interests became aware of The People reports.
"KC did not know how she became aware of them or what the effect would be, which caused our client great concern and anxiety", said Mr Dingemans.
Ms Rogers said on behalf of MGN that the publishers had done nothing other than promptly acknowledge the error that had been made.
There were no deliberate delays, and MGN was motivated by the wish to put the error right.
The words KC complained of were not published prominently but were in the eighth and 24th paragraphs of a crime supplement that focused plainly on Tracey Connelly. There was no repetition online or elsewhere.
MGN had given the published apology greater prominence in the newspaper than the article and set the record straight "beyond any doubt", argued Ms Rogers.
The apology and correction vindicated KC's reputation.
He had been offered "a substantial sum of damages" over the publication, but he had refused it.
KC was not named in the article, and, as his anonymity remained protected, there was no photograph or other image enabling people in the street "to point the finger" at him, said Ms Rogers.
His uncle had been the first to telephone him about the article, but KC did not suggest that his uncle thought it other than a mistake.
It was to be expected that his family and friends would know that he had no criminal convictions.
The case was "nowhere near the top of the range" where very serious allegations had been made, repeated and unsuccessfully defended.
Reserving judgment, Mr Justice Bean said he would hand down his decision "as soon as I can".