Alfie's parents claimed the hospital had applied to the High Court to remove parental rights and withdraw ventilation.
The parents of a 23-month-old boy at the centre of a life-support treatment battle have lost their latest legal battle to have their child treated overseas.
The court ruled that his life support won't be turned off until the Supreme Court has reached its decision.
Police have increased security at the children's hospital in Liverpool in fear of angry protests from the parent's supporters, who have dubbed themselves "Alfie's Army".
Alfie, from Bootle, Merseyside, has been at Alder Hey since December 2016 with an undiagnosed degenerative brain disease.
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.
"We're never going to give up on you, Alfie".
Their case is being heard by three appeal court judges in London.
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"As has been determined with considerable clarity in this case, Alfie's best interests are determinative and the court has decided what treatment he should or should not receive".
Alder Hey Children's Hospital said in a statement: "At each stage of the legal process the courts have agreed with expert advisers... that Alfie's condition is untreatable". Courts have refused to allow the parents to determine what is in Alfie's best interest.
The justice also stated that it is "wrong to say that the parents' own views can trump that judicial determination".
Alfie's parents made one last legal attempt to wrest control over the treatment of their son at the Court of Appeal.
The family have been encouraged by Alfie's Army - a grass root social media campaign - and their plight was acknowledged in tweets from Pope Francis. Supporters have since demonstrated outside the hospital and bosses have pleaded with those assembled not to disturb staff or patients.
Alfie's parents said they believed he was still responsive to them, and his father told reporters outside court his boy was "improving". The judge said detail of that plan could not be revealed because Alfie was entitled to privacy at the end of his life.