I must admit that I haven't been closely following reports on the medical details or on the legal proceedings. I don't know if it was established beyond doubt that he was "brain dead" (supposing that this can be established beyond doubt).
Here is part of an article from 13 June:
A judge has ruled that a 12-year-old boy with catastrophic brain damage is dead and that his treatment can stop. ... On Monday Mrs Justice Arbuthnot, sitting in the family division of the high court, backed doctors at the Royal London hospital in east London who concluded that Archie was “brain-stem dead” and should no longer be kept alive. She said doctors could lawfully stop treating him.
A more recent one:
After being transferred to the Royal London Hospital in east London, run by Barts Health NHS Trust, doctors told Archie's family they believed his brain damage was so significant that he may be brain stem dead.
Doctors asked to conduct a brain stem death test, but Archie's family denied consent, leading the trust to bring a case at the High Court in London for permission for the test to be carried out.
In subsequent hearings, lawyers representing the trust had asked the judge to decide what moves were in Archie's best interests.
The brain stem test was unable to be conducted and since further hearings have taken place to determine whether life-sustaining treatment should continue.
At the end of a hearing on 13 June, the judge ruled that Archie had died on the day of his MRI scan on 31 May and his life support treatment could stop.
Lawyers representing the hospital's governing trust, Barts Health NHS Trust, had told Mr Justice Hayden that Archie had suffered a "devastating" brain injury. ... Mr Justice Hayden said evidence showed that Archie had suffered a "significant injury" to "multiple areas" of his brain and had not "regained awareness at any time". ...
He said medical evidence had shown that improvement in Archie's condition was "not possible" and there was "no hope at all of recovery".