The parents of Archie Battersbee - the 12-year-old boy left in a comatose state after suffering brain damage - have failed in their bid to persuade the Supreme Court to intervene in his life-support treatment battle.
They had asked Supreme Court justices to give them more time to carry on their fight.
Ms Dance and Mr Battersbee, who are separated but both live in Southend, Essex, want the United Nations to consider the case after losing life-support treatment fights in London courts.
They appealed to Supreme Court justices on Thursday to block hospital bosses from withdrawing life support treatment until they have had time to make an application to the UN.
But three justices at the Supreme Court refused to give the family permission to appeal.
A Supreme Court spokeswoman said the court had received "an urgent permission to appeal (PTA) application" from Archie's parents earlier in the day.
"They were seeking a stay of the Court of Appeal’s decision to allow withdrawal of life-support treatment from their child.
“Aware of the urgency of this matter, the court convened a panel of three justices who considered submissions from the parties ‘on paper’, in the usual way.
“Having considered the careful judgment of the Court of Appeal delivered by Sir Andrew MacFarlane (president of the Family Division) and the application for permission to appeal the Court of Appeal’s decision in relation to the stay, the panel has refused permission to appeal to the Supreme Court.”
Archie’s parents say the UN has a protocol which allows “individuals and families” to make complaints about violations of disabled people’s rights.
They say the UN could ask the UK government to delay the withdrawal of life support to Archie while a complaint is investigated.
What's happened this week?
Appeal court judges on Monday upheld a ruling that Archie's life support treatment could lawfully be stopped, after the health trust caring for him asked the court to rule on his best interests.
His family had asked for a postponement to the hearing after Archie's father had a suspected heart attack shortly before the hearing and gone to hospital. He has now been released.
Lawyers representing Archie’s parents then asked appeal judges to “stay” - or delay - the end of treatment to allow time for to consider applying to the European Court of Human Rights (EHCR) in Strasbourg, France, which was granted until 2pm on Thursday.
The Christian group representing the family, Christian Legal Centre, claimed this "stay" prevented the family from applying to the UN - which is Archie's parents' preferred option.
They had asked the Supreme Court to "stay the execution of the order which authorises withdrawal of life support from Archie,” a spokesman said.
“This is to enable the parents to take their case to the UN Committee on the Rights of Persons With Disabilities.”
He added: “The UK has joined the Optional Protocol to the UN Convention on the Rights of Persons with Disabilities, which gives individuals a right to complain about any violations of the Convention to the UN Committee.
“The committee has previously criticised the UK system of authorising withdrawal of life support from disabled people based on the court determination of their best interests rather than on their own wishes.
“The family’s lawyers will argue that, by making a stay which only allowed an application under the ECHR, the Court of Appeal wrongly subjected the family to pressure not to adopt one international human rights procedure over another.”
What happened to Archie Battersbee?
Archie suffered “catastrophic” brain damage in an accident at home three months ago.
His mother found Archie unconscious with a ligature over his head on 7 April. She thinks he may have been taking part in an online challenge.
The youngster has not regained consciousness.
Doctors treating Archie at the Royal London Hospital in Whitechapel, east London, think he is “brain-stem dead” and say continued life support treatment is not in his best interests.
Archie’s parents disagree and say his heart is beating, and are being supported by the campaign group the Christian Legal Centre.
Lawyers representing the Royal London Hospital’s governing trust, Barts Health NHS Trust, had asked for decisions about what medical moves are in Archie’s best interests.
Another High Court judge, Mrs Justice Arbuthnot, initially considered the case and concluded, after an earlier hearing, that Archie was dead.
But Court of Appeal judges upheld a challenge by Archie’s parents against decisions taken by Mrs Justice Arbuthnot and said the evidence should be reviewed.
At a second hearing, Mr Justice Hayden said evidence shows Archie suffered a “significant injury” to “multiple areas” of his brain and had not “regained awareness at any time”. He said the reality of Archie’s case was “terrible”.
But his family also appealed that decision arguing that Mr Justice Hayden had not given “real or proper weight” to the wishes and religious beliefs of Archie or his family, and had failed to carry out a “comprehensive evaluation” of the benefits and burdens of continuing life-support treatment - an appeal rejected by the Court of Appeal on Monday.
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