The parents of brain-damaged 12-year-old Archie Battersbee have failed to persuade the Supreme Court to intervene in his life-support treatment battle.

The boy’s mother and father, Hollie Dance and Paul Battersbee, had asked Supreme Court justices to give them more time to carry on their fight, possibly taking it to the UN.

But the judges’ decision means the hospital trust can now legally withdraw his medical treatment at any time.

The family’s lawyer has told Sky News Archie’s parents still plan to try to take the case to the UN or the European courts.

It comes after the Court of Appeal earlier this week upheld the High Court’s decision to withdraw life-support treatment for the boy.

The Supreme Court said it “has great sympathy with the plight of Archie’s devoted parents and recognises the emotional pain which they are suffering” but after careful consideration has refused to give them permission to appeal the Court of Appeal’s decision.

Mr Battersbee and Ms Dance want the UN to consider Archie’s case, arguing it has a protocol that allows “individuals and families” to make complaints about violations of disabled people’s rights.

They claim the UN could ask the UK government to delay the withdrawal of life support while a complaint is investigated.

Archie has relied on mechanical ventilation since being admitted to hospital on 7 April, after being found unconscious with a ligature around his neck at home in Southend, Essex.

Doctors treating him at the Royal London Hospital in Whitechapel, east London, say he is brain-stem dead and continued life-support treatment is not in his best interests.

Barts Health NHS Trust wants to withdraw treatment and was last week granted permission to do what the High Court ruled was best for Archie.

The court ruled in favour of removing life support in June after a test showed he was dead.

On Monday, Court of Appeal judges said doctors could lawfully stop providing the treatment and the youngster could be disconnected from a ventilator.

The family argue that stopping treatment would be in breach of the UK’s obligations under Articles 10 and 12 of the UN Convention on the Rights of People with Disabilities, and Article 6 of the UN Convention on the Rights of Children.

These international obligations say states must take all necessary measures to ensure disabled people enjoy equal rights and that governments should do all they can to prevent the deaths of children and young people.