The parents of a brain-damaged baby who tried to breathe after doctors said he was dead have failed in appeal bids after losing the latest stage of a life-support treatment fight and are “devastated”, a lawyer has said.

A High Court judge recently ruled that ending life-support treatment is lawful and in the five-month-old boy’s best interests.

Mr Justice Poole, who reconsidered evidence at the latest in a series of hearings in the Family Division of the High Court in London, said treatment is “futile”.

Solicitor Amy Rowe, who represents the couple and works for law firm Dawson Cornwell, said appeal judges refused to overturn Mr Justice Poole’s decision.

The couple made written applications to the Court of Appeal in London and the European Court of Human Rights in France, but both bids had been rejected, Ms Rowe said.

She told the PA news agency: “My clients and their family are understandably devastated.”

The couple lost an earlier High Court fight; Mr Justice Poole oversaw a second trial after they successfully appealed.

Lawyers representing Guy’s and St Thomas’ NHS Foundation Trust, which is responsible for the boy’s care, had asked for decisions about what moves are in his best interests.

The boy, who will be six months old on Friday and is in a specialist unit at a London hospital, was found unresponsive in June, judges have heard.

Doctors said his brain was starved of oxygen for over 30 minutes and he suffered “devastating” brain damage.

Specialists said the boy, who is on a ventilator, has no prospect of recovering. They said he should be taken off the ventilator and given palliative care.

The boy’s parents, who are Muslims of Bangladeshi origin, urged the judge to give him more time to “make progress” or for “Allah to intervene”.

My clients and their family are understandably devastated

Mr Justice Poole oversaw a private hearing but allowed reporters to attend.

He said the case can be reported but neither the boy nor medics involved in his care can be identified in media coverage.

He was told the boy’s parents were interviewed by police after evidence suggested he suffered what appeared to be “non-accidental injuries”.

No charges had been brought but the couple remained under investigation.

The boy was declared dead in June after doctors diagnosed him as brain-stem dead, the judge heard.

He remained on a ventilator because his parents were unhappy with the diagnosis and litigation had begun.

A nurse subsequently noticed him trying to breathe.

Another High Court judge, Mr Justice Hayden, had earlier decided that treatment should end.

The parents represented themselves at a trial overseen by Mr Justice Hayden.

Appeal judges concluded that Mr Justice Hayden should have adjourned the trial to give them time to find lawyers.

Barristers Victoria Butler-Cole KC and Arianna Kelly, and Dawson Cornwell, represented the couple free of charge at the trial overseen by Mr Justice Poole.

:: The mother of a severely disabled five-year-old girl is embroiled in a High Court life-support treatment fight.

Doctors say ending treatment is in the youngster’s best interests. The girl’s mother disagrees.

Mr Justice Hayden began considering evidence at a hearing in the Family Division of the High Court on Wednesday.

The Great Ormond Street Hospital for Children NHS Foundation Trust, in London, has responsibility for her care and bosses have asked for a ruling on what moves are in her best interests.

Mr Justice Hayden said the girl, who is receiving ventilation, cannot be identified in media reports.

A judge is due to oversee a trial on Friday.

Mr Justice Hayden has overseen a number of child life-support treatment cases in recent months.

In July, he ruled that doctors could lawfully stop providing life-support treatment to a 12-year-old boy who suffered brain damage in an incident at home in Southend, Essex, in April.

Archie Battersbee died after his mother, Hollie Dance, and father, Paul Battersbee, failed in bids to overturn Mr Justice Hayden’s ruling.