He rejected claims by Alfie's father, Tom Evans (21), that his son was "significantly better" than first thought because he had now been breathing unaided for 20 hours after doctors first withdrew life support on Monday night at Alder Hey Children's Hospital in Liverpool.
The judge, however, ruled that this would not be within his best interest and he would not be allowed to travel to Rome or Munich, where another hospital had offered to treat him.
A petition asking the Queen to intervene and help save brain-damaged Alfie Evans has gathered more than 110,000 signatures in just over two days.
Mr Justice Hayden ruled out his family's wishes to take the child to the Bambino Gesu hospital in Rome, following interventions from the Pope and the Italian authorities.
Doctors have been left "gobsmacked" after Alfie's life-support was withdrawn but he continued to live, his father Tom Evans has said.
On Tuesday, according to lawyers representing Alfie's family, a British judge sided with the doctors, saying that the family can not accept the offer to take Alfie to the Vatican for treatment.
A spokeswoman for the Christian Legal Centre, representing Alfie's parents, said their appeal is due to be heard at the Court of Appeal on Wednesday afternoon.
However, an earlier court ruling by Lord Justice Hayden, upheld twice by the highest courts in the United Kingdom, expressly forbids the seriously-ill youngster from being removed from the hospital.
"A brain can not regenerate itself, as I have been told".
"There is, in truth, with great respect to the efforts of (parents' lawyer) Mr Diamond, no substance to this application, which represents, at least within the court process, the final chapter in the case of this extraordinary little boy".
Before the hearing, a spokeswoman from Christian Legal Centre said: "Alfie has survived much longer than the doctors predicted, lending support to the request from Alfie's parents for Alfie to be seen by medical experts in Italy".
Speaking to reporters outside Alder Hey hospital in Liverpool, dad Tom said: "Both Kate and I had to give him mouth to mouth resuscitation to keep him alive because his lips turned blue".
He also praised the hospital's "world class" care of the child.
But Alfie's doctors say he can not be healed, and shouldn't make the trip at all.
Americans will hold a vigil in support of Alfie Evans outside the British embassy in Washington, D.C. on Thursday, April 26 at 11:00 a.m.
The child's parents, Liverpudlians Tom Evans and Kate James, had asked for a delay.
Last night life-support was withdrawn but Alfie, who has a degenerative neurological condition destroying his brain, has shocked medics by continuing to breathe unaided for almost 24 hours with an air ambulance on stand by to fly the child to Italy.
But his parents have fought a long battle to ask the courts to allow them to take him overseas.
The family's appeal was rejected as "inadmissible" by the European Court of Human Rights.
"An air ambulance is now waiting outside Alder Hey Hospital ready to take Alfie to hospital in Italy".
He is now being hydrated and given oxygen to stop him becoming distressed.