Last week, the high court judge Mr Justice Hayden endorsed a detailed plan put forward by Alder Hey doctors for withdrawing life-support treatment.
Mr Evans and Ms James asked Court of Appeal judges to rule that the toddler should be allowed to receive treatment in Italy.
In further accusations, Alfie's mother was allegedly asked to leave Alfie's bedside after she questioned hospital visiting rules with supporters, known as Alfie's Army, tweeting on Friday: "Alfie's mummy's been told to leave Alfie's side and removed from the ward for asking the nurse is it acceptable for family members now being told they can not see Alfie".
Mr Evans begged in an earlier Facebook post: "Can I ask that after tonight I would really appreciate if everyone has a break from the protesting please?"
"We just wanted to take our son to give him the chance he deserves".
Chief Inspector Chris Gibson said officers "recognise the sensitivities involved in this very hard and sad situation".
As the hearing began there were more protests outside the hospital by people dubbing themselves "Alfie's Army".
"This is extremely unhelpful for all concerned and we are investigating further to establish the full circumstances".
On Monday Court of Appeal judges Lord Justice Davis, Lady Justice King and Lord Justice Moylan ruled against the parents in London.
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Supreme Court justices might be asked to consider the case for a second time after Alfie's parents, who live in Liverpool, used a piece of ancient English common law in their legal battle.
Two hours after Monday's decision was made in London, Mr Evans emerged from the hospital.
"I will update you on where we go from here and if we get permission then that would be a good reason to demonstrate peacefully".
Doctors have said they can provide no further treatment for the little boy, but his parents, Tom Evans and Kate James, have fought against the decision.
Judges have heard that Alfie, born on May 9 2016, is in a "semi-vegetative state" and has a degenerative neurological condition doctors had not definitively diagnosed.
In a statement, Alder Hey Children's Hospital said it trusted that "the public and supporters of Alfie's parents will read in detail the decision of the Court of Appeal following today's hearing".
The legal battle between Alfie Evans' parents and doctors comes as Alder Hey, one of only four specialist children's hospitals in England, was found to have failed four in five standard checks during an unannounced inspection, The Guardian reported Saturday.
In statement Alder Hey said it "refuted" criticisms from Mr Evans of the treatment Alfie has received.
It added: "Our priority is to continue to provide the best possible care for Alfie and his parents at this hard time".