In February, Mr Justice Hayden ruled that doctors at Alder Hey could stop treating Alfie against the wishes of his parents following hearings in the Family Division of the High Court in London and Liverpool.
Hundreds of protesters backing Alfie's parents have been demonstrating outside the Alder Hey Children's Hospital in Liverpool for several days amid a legal battle over the 23-month-old's care.
'We will never give up on you Alfie'.
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.
At the appeal hearing, Lord Justice Davis said doctors had agreed that there was "no hope" for Alfie.
Alfie Evans, from Liverpool, is on a life support machine and requires round-the-clock treatment at Alder Hey Children's Hospital in the city.
Supreme Court justices and European Court of Human Rights judges have refused to intervene.
Shortly after the statement, Evans posted a video on Facebook of Alfie's hospital room, from which he said patients could only hear the noise outside if the window was opened.
He said details of that plan could not be revealed because Alfie was entitled to privacy at the end of his life.
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The legal battle between Alfie Evans' parents and doctors comes as Alder Hey, one of only four specialist children's hospitals in England, was found to have failed four in five standard checks during an unannounced inspection, The Guardian reported Saturday.
The couple have now asked the three appeal judges to overturn decisions made by Mr Justice Hayden last week.
Mr Justice Hayden said flying Alfie to a foreign hospital would be wrong and pointless.
Mr Hayden refused that request.
The judge also dismissed that suggestion.
"Whilst many people have gathered to protest in a peaceful way, Merseyside Police is now investigating a small number of reports, some of which originate from social media, as well as instances of verbal abuse and acts of intimidation from those outside the hospital", he added. "Loud and constant noise, such as from vehicle horns, affects sleep and raises anxiety levels for our patients, especially when recovering from procedures, so please bear them in mind".
But a spokesman insisted that the hospital remained fully operational. The parents want to move him to a hospital in Rome or Germany.
In statement Alder Hey said it "refuted" criticisms from Mr Evans of the treatment Alfie has received.
Mr Evans and Ms James say "the state" is wrongly interfering in their parental choices.
Judges have heard how Alfie, born in May 2016, is in a "semi-vegetative state" and has a degenerative neurological condition that doctors have been unable to diagnose definitively.
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