Mr Evans and Ms James say "the state" is wrongly interfering in their parental choices.
Baby Alfie Evans' father Tom delivered a defiant message to Alder Hey Children's Hospital after a United Kingdom judge rejected the parents' latest bid to save their son's life.
As news from the court filtered through to Alfie's supporters at the hospital, tears mixed with anger and police officers fanned out around the crowd, who began a chant of "Save Alfie Evans!".
"What we can't have is a sort of legal "groundhog day" where you come back again and again on the same basis".
The toddler's family have said they are accompanied by their own doctors, have removed duty of care from the hospital and placed it with their air ambulance, and have a jet ready to take the child to Italy.
Court of Appeal judges upheld his decisions.
Most of the protesters have now moved from outside the hospital's main entrance to Springfield Park, a short distance away.
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"It's not over", Tom said.
Alfie, born in May of 2016, suffers from an unknown neurological degenerative condition which hospital staff say has reduced him to a vegetative state and corroded his brain matter.
Appeal court judges said doctors should continue treating Alfie pending a Supreme Court decision. "It is precisely because of this judicial determination that Aflie has been kept in Alder Hey Hospital", Moylan said.
He also dismissed the suggestion that Alfie was being unlawfully detained an Alder Hey and refused to grant a writ of habeas corpus. The court expressly determined that it would be lawful, because treatment would be in Alfie's best interests and that no other available course would be.
Mr Diamond is also arguing there is "no legal right" to keep the young boy at the hospital, despite police blocking attempts by the boy's father to remove him from the hospital.
The parents lost their bid to allow Alfie to be taken overseas for treatment.
One protester said: "He's still fighting so we're still fighting".
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Supreme Court justices and European Court of Human Rights judges refused to intervene.
Last week, a judge decided it was in the best interests of Alfie for his life support to be switched off.
Save Alfie Evans! Tell the hospital to let his parents take him home.
Evans' mention of the hospital not allowing the family to be together was in reference to a letter he shared last week in which Alder Hey accused pro-Alfie protesters of causing "significant disruption" to other patients' families and staff.
As for Alfie's future prospects, staff at Bambino Gesu have offered to perform a tracheotomy to improve his aided breathing and a percutaneous endoscopic gastrostomy so that he can be fed through his stomach.
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Newspaper Gazzetta dello Sport branded Oliver "not up to standard". "Also the red to Buffon for vehement protests was excessive". Buffon added on Saturday he "stands by everything he said", before adding, however, that he "would use different tones".