Channel 4 breached broadcasting guidelines with jokes about Katie Price's son Harvey on its Frankie Boyle comedy show, the media regulator has ruled.
The watchdog received hundreds of complaints about the comments aired on the controversial series Tramadol Nights.
Boyle said that Price married cage-fighter Alex Reid because she needed someone strong enough to protect her from her son's sexual advances.
He also joked that Price and her ex-husband Peter Andre didn't want to keep Price's son, and were fighting each other over who would not gain custody.
Harvey, who is large and strong for his age, suffers from physical and mental conditions and needs constant care.
Former glamour model Price complained that the comments, broadcast in December last year, were "discriminatory, offensive, demeaning and humiliating".
Channel 4 defended the comments, adding that its job was to champion and pioneer "distinctive voices in British comedy and bring them to a wider audience".
It said that viewers were given strong warnings about the show, which started at 10pm, an hour after the watershed.
It denied that the joke about Price and Harvey was about Harvey's disability, or about rape or incest, saying it was "simply absurdist satire".
The broadcaster said that Price had already put her child in the public eye, had sparked complaints about being too sexually explicit in front of her children in her own reality show, and that her new husband Reid - who she has since split from - "made a series of public jokes about Harvey resembling the fictional character The Incredible Hulk".
The broadcaster said it was "these specific remarks and the general high profile of the child, that Frankie Boyle's joke is predicated upon".
It said that the joke about custody was not about Harvey but "aimed clearly at Katie Price and Peter Andre, painting them as cynically exploiting a child in custody proceedings in the media."
But Ofcom said that any "intended satire in the two comments was ... obscured by their straightforward focus on Harvey Price and his disability."
It accepted that Price, Reid and Andre "have consciously exposed their and their children's lives to the media".
But it said that this did not justify humour targeted at a child's expense, especially when the child is "as young as eight years old, and has a number of disabilities which are specifically focused on as the target of that intended humour".
The jokes appeared to "directly target and mock the mental and physical disabilities of a known eight-year-old child who had not himself chosen to be in the public eye", it said.
It added: "Frankie Boyle's comments appeared to derive humour by demeaning the physical and mental disabilities of a known eight-year-old child."
It said the broadcaster had attempted to comply with the broadcasting code, and that the broadcast was an "erroneous decision on a matter of editorial judgment on the broadcaster's part".
Complaints about other sketches in the series were not upheld.
Channel 4 said in a statement that it "acknowledges Ofcom's findings in relation to Frankie Boyle's Tramadol Nights and his comments about Katie Price.
"We welcome their finding that we were not in breach of the code regarding any other sketches or jokes within the series," a spokesperson added.
Price later criticised Ofcom for not forcing the broadcaster to air an apology and said Channel 4's role as official UK broadcaster of the 2012 Paralympics should be questioned in the light of the finding.
She said: "While I am pleased that Ofcom have ruled against Channel 4 and I understand that they consider this ruling itself to be a sanction against the broadcaster, I am amazed that Ofcom have not required, at the least, an apology to be broadcast.
"This strikes me as a further insult to my wonderful son and another in a series of failures in this sordid affair."
Ofcom and Channel 4's response was "sadly symptomatic of how disability is treated in our society and should not be accepted", she said.
She added: "Channel 4 attempted to justify their actions to Ofcom ... by attacking me.
"This issue is not and never was about me. It was about a direct attack on a disabled eight-year-old child by a national broadcaster (which let us not forget is to be the official broadcaster for the 2012 Paralympics - a role which should be questioned in light of this finding).
"Given Channel 4's failures, I can't help but feel Ofcom have let Harvey and disabled people in general down by not requiring Channel 4 to apologise.
"Would they have taken this route if Harvey was the child of a well-known politician?
"It is clear that people at the highest levels in Channel 4 made a major misjudgment and that they are not capable of seeing how wrong their behaviour was."
Mencap head of campaigns and policy David Congdon said: "We are pleased Ofcom has upheld the complaints against Channel 4 and Frankie Boyle and found that they breached broadcasting guidelines.
"However, Channel 4's response is baffling, particularly the comments ... about their programming 'testing the boundaries'.
"Given the number of stories Mencap hears on a daily basis about people with a learning disability being made the butt of jokes, called names, harassed and experiencing physical violence, this so-called joke is far from 'edgy' or 'absurdist'.
"Hearing comments and 'jokes' like Frankie Boyle's is unfortunately a common reality for people with a learning disability."
Tom Pey, chief executive of the Royal London Society for Blind People, said: "It is incumbent now on Channel 4 to apologise."
He added: "The chief executive of Channel 4 David Abraham should now resign. His position is untenable."
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