A High Court judge began analysing preliminary issues in the case at a hearing in the Family Division of the High Court in London on Tuesday. His doctors say that he has an undiagnosed neurological condition that has resulted in serious and irreparable brain damage. He died on July 28 shortly before he would have been a year old.
In addition, the court also approved the Liverpool hospital's plan to gradually withdraw treatment. "No application to the European Court of Human Rights in Strasbourg can or should change that". The parents want to take their son to be treated at a hospital in Rome and hundreds of people protested outside the hospital last week when his father asked staff to release the boy.
Alfie's parents wanted to move their son from Alder Hey to a hospital in Rome.
The couple said Italian doctors were willing to treat the little boy and an air ambulance was available.
The court also refused permission for Mr Evans and Ms James with appeal the decision.
Alfie's parents filed a petition to the Supreme Court after the UK Court of Appeal ruled this Monday against the parents' argument that their son was being unlawfully detained by the hospital.
A writ of habeas corpus - Latin for "you may have the body"- is a legal manoeuvre which requires a court to examine the legality of a detention. However, they were unsuccessful in overturning Mr Justice Heydon's February 20 decision.
The decision was announced on Friday by Supreme Court president Lady Hale, Lord Kerr and Lord Wilson.
Judges in the case said the hospital must be "free to do what has been determined to be in Alfie's best interests" and there was "no reason for further delay".
The 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 nearly all of his brain has been destroyed".
Alfie's parents have done everything in their power to do what they think is best for him even though that is contrary to the views of the doctors.
"Those of us who have to deal with this case dispassionately as a point of law can feel for their sadness".