Mr Evans and Ms James asked Court of Appeal judges to rule that the toddler should be allowed to receive treatment in Italy.
The parents of a 23-month-old boy at the centre of a life-support treatment battle have lost their latest legal battle to have their child treated overseas.
Alder Hey doctors say continuing to treat Alfie is "unkind" and "futile" but his parents want to take him to a hospital in Rome and say they have a private ambulance and jet on stand-by.
The decision was then upheld by the Supreme Court and the European Court of Human Rights.
Last week, Mr Justice Hayden endorsed a detailed plan put forward by Alder Hey doctors for withdrawing life-support treatment - after considering a number of issues at a follow-up High Court hearing.
Police have increased security at the children's hospital in Liverpool in fear of angry protests from the parent's supporters, who have dubbed themselves "Alfie's Army".
Trump lawyer Cohen expected at court hearing, Stormy Daniels to attend
Cohen has admitted to paying adult film star Stormy Daniels $130,000 to keep quiet about an alleged affair with Trump. The FBI executed search warrants last week on Cohen's office, home, security deposit box and hotel room.
The 23-month-old has an undiagnosed degenerative brain condition and has been in care and on ventilation at Alder Hey Children's Hospital in Liverpool since December 2016. He argued that it was a deprivation of Alfie's liberty in not letting him travel to a different hospital.
"The bad reality was that nearly the entirety of Alfie's brain has been eroded, leaving only water and cerebral spinal fluid", Moylan said, reading from Hayden's previous decision, according to The Sun. The court expressly determined that it would be lawful, because treatment would be in Alfie's best interests and that no other available course would be.
In addition, Moylan said it is "wrong to say that the parents' own views can trump that judicial determination", according to LifeSiteNews.
Moylan also addressed Tom's attempt to remove Alfie from the hospital on Wednesday with the aid of foreign medical staff on the advice of Pavel Stroilov of the Christian Legal Centre.
The couple took their case to the Supreme Court on 20 March where justices refused to give the couple permission to mount another appeal.
"We fully understand what a sensitive and emotional time this is for everyone involved and I would also therefore like to pass on our appreciation for the way in which Alfie's family were later able to speak to the crowd and offer assurance and calm".
- California rejects Trump administration plan for National Guard troops on border
- Sri Lanka joins Commonwealth alliance to fight against plastic pollution
- Why Investors remained buoyant on: Microsoft Corporation (NASDAQ: MSFT)
- Allegiant Air Had More Than 100 Big Problems in 2 Years
- NBN-related complaints to TIO jump by 200%
- Russian Federation says Britain staged alleged Syria chemical attack
- Tax Day 2018: Where you can cash in on freebies and deals
- Google testing iPhone X-style gesture navigation in Android P?
- Knight Riders slay Daredevils
- VAR chaos strikes again as Bundesliga referee hands Mainz 'half-time' penalty