The parents of a seriously ill toddler from Liverpool are fighting a court ruling allowing medics to withdraw his life support.
Tom Evans, 21, and Kate James, 20, had asked Court of Appeal judges to rule that 23-month-old Alfie could go overseas for treatment.
He sought to overturn Mr Justice Hayden's decision last week that Alfie's parents may not remove him from Alder Hey hospital.
A United Kingdom judge denied an appeal from Alfie Evans' parents Monday to have him treated outside the country, saying their parental rights did not matter.
The 23-month-old has an undiagnosed degenerative brain condition and has been in care and on ventilation at Alder Hey Children's Hospital in Liverpool since December 2016.
He then alleged the hospital called the police to prevent him removing his son, with officers allegedly telling him he would be "arrested for assault" if he attempted to remove Alfie.
Their case is being heard by three appeal court judges in London. Moylan, however, disagreed on the basis that the court had already decided that it was in Alfie's best interest to remain at Alder Hey hospital.
In addition, Moylan said it is "wrong to say that the parents' own views can trump that judicial determination", according to LifeSiteNews.
Mr Hayden said the unanimous view of medical experts was that Alfie's brain had been eroded by disease and further assessment was pointless.
However, Alder Hey said in a statement: "Noise from recent protests has unfortunately affected our patients so we would ask that noise levels outside the hospital are kept to a minimum and, for example, auto horns are not sounded".
The parents do, however, have the right to directly ask the Supreme Court for permission to appeal. Courts have refused to allow the parents to determine what is in Alfie's best interest.
The judges rejected their application but said that they could go to the Supreme Court to consider the case for a final time.
Speaking outside the hospital, Alfie's dad declared "it's not over" while crowds of supporters chanted "get him out".
That hearing came after Alfie's parents failed to reach an agreement with Alder Hey bosses about their son's end of life plan. The hospital issued a statement asking the protesters to lower the volume of their demonstrations and to stop honking their vehicle horns since it was disturbing some of the patients, according to The Guardian.