The parents of terminally ill toddler Alfie Evans have lost the latest stage of their legal battle over his life support.
Tom Evans and Kate James failed to persuade the Supreme Court that Alfie was being unlawfully detained at Alder Hey Children's Hospital in Liverpool.
The court also refused permission for the parents to appeal the decision.
But Mr Evans said they would not give up and had made an "urgent application" to the European Court of Human Rights.
Judges said the hospital must be "free to do what has been determined to be in Alfie's best interests".
The Supreme Court has also approved a plan for withdrawing treatment and bringing the 23-month-old's life to an end.
The judges said there was "no reason for further delay" and "there will be no further stay of the Court of Appeal's order".
"That is the law in this country. No application to the European Court of Human Rights in Strasbourg can or should change that," they said.
The couple had made another application to the Supreme Court after losing a second fight over Alfie at the Court of Appeal.
They wanted to take Alfie - who has been suffering from an undiagnosed degenerative brain disease - to a hospital in Rome where he would continue to receive palliative care.
Alfie's parents had already lost a first round of cases in the High Court, Court of Appeal, Supreme Court and European Court of Human Rights.
Speaking outside Alder Hey, Mr Evans said: "This is not justice. This is a cruel bureaucracy.
"We have instructed our lawyers to submit an urgent application to the European Court of Human Rights, and they have done so today.
"We will not give up. We will continue to fight, by all means available to us within the law, to save our son's life."
The Supreme Court justices said: "Alfie looks like a normal baby, but the unanimous opinion of the doctors who have examined him and the scans of his brain is that almost all of his brain has been destroyed.
"No-one knows why. But that it has happened and is continuing to happen cannot be denied.
"It means that Alfie cannot breathe, or eat, or drink without sophisticated medical treatment. It also means that there is no hope of his ever getting better."
Earlier this week Mr Evans flew to Rome to meet Pope Francis and begged him to "save our son".
A statement issued by Alder Hey reiterated today's Supreme Court ruling, adding: "We understand that this decision is very distressing for Alfie's family at this very difficult time."
Andrea Williams, chief executive of the Christian Legal Centre, which is now representing Alfie's family, said: "We are going to appeal to the European Court of Human Rights hoping we can stay the end-of-life order our courts have made.
"We are appealing today because we have got to act quickly. The parents are devoted parents."
Ms Williams added: "It is one thing to argue any medical treatment is futile, it is quite another thing to say someone should die because their quality of life is futile."
Last week Merseyside Police said it was investigating "acts of intimidation" among protesters outside Alder Hey after the atmosphere outside the hospital was described as "intimidating and scary".