The pair appeared on the show to debate the controversial method, the theories of which date back to the 1960s but which has recently been gaining momentum across Britain.
Mum-of-two Peaches championed the child-rearing movement, which states that a child should be kept close its mother at all times to ensure their needs are met immediately, and usually involves parents and children sleeping in the same bed and longer breast-feeding periods.
Katie, meanwhile, described attachment parenting as "new-age" nonsense, saying "Attachment parents are c**p parents".
The confrontation actually began before the show began, with a heated Twitter exchange between the two ladies.
Katie antagonised Peaches by posting a picture of her son Astala falling out of his pram, with the caption, "Peaches believes in attachment parenting. Attached to a phone that is."
The 24-year-old was quick to respond to the former Apprentice star.
'I don't even want to reply to Katie Hopkins desperate, incessant tweeting because it feeds her insatiable lust for recognition," she wrote. "However her posting low blows like a picture of my son falling from his pram when I tripped over a crack in a pavement has warranted at least a few responses from me."
"…This is the woman who hates women, ethnic minorities, anyone with less money, anyone who dares point out the glaringly obvious about her own children on a regular basis."
She went on to say of Katie, who has become known for her controversial and lively discussions on This Morning, "What we need to ask ourselves is why we even allow her to have a platform.
"It says a lot about the state of current media that she is allowed to spew her repugnant hate all over day time tv shows. I'm all for free speech, but when a woman who insults the disabled is the current fave in a long line of ever changing "love to hate" tabloid darlings."
Immediately after their on-air debate, Peaches returned to Twitter to claim victory. "Well… That was easy. Think I know who won the one. Hopkins was literally SHAKING when I shook her hand afterwards.
She also posted a picture of the pair together, with the caption, "I think we all know who won. She was quaking in her Sloanie old boots. The panto witch finally met her match!"