The judge in the case of the desperately sick baby Charlie Gard has said he is open to a change of mind –  but only if there is new evidence that supports it.

Mr Justice Francis told the court this morning: 'If there is important evidence which suggests that I should change my position, then I will change it.' He said he would need to be persuaded that 'something new or dramatic has changed.'

And in dramatic scenes at court, the parents of baby Charlie, Chris Gard and Connie Yates, stormed out of the court after disagreeing with the judge about what they said in court at an earlier hearing three months ago. 'This is supposed to be independent,' muttered Chris when the judge said the parents themselves had stated Charlie had no quality of life.

Passing car drivers tooted their horns as protesters, pro-life campaigners and family supporters chanted outside the High Court today in an impassioned attempt to persuade the judge to allow Charlie, 10 months, a shot at treatment in the United States. 

Charlie has a rare and potentially fatal illness, mitochondrial DNA depletion condition, but Chris and Connie believe a new experimental treatment being developed in the United States could save his life.

They are appealing in court against a decision that doctors at Great Ormond Street Hospital can switch off his ventilator and have raised more than £1.3 million for his treatment in the US. They've already lost numerous court appeals but a final hearing was allowed that began yesterday as the parents said they had new information that they believe could change the judge's mind.

After the European Court of Human Rights refused to allow the parents to intervene, both US President Donald Trump and Pope Francis stepped in with offers of support. 

Family spokesman Gawain Towler told Christian Today the family is hoping they will be allowed to take Charlie to a hospital in the US to try and experimental treatment. 

'They are hoping they will be allowed to take Charlie for the ground-breaking treatment that is available in the US but not here,' he said.

'The right to life is not a specifically Christian concept. This is an ethical issue that crosses all religions – and none.'

He said he did not blame the doctors and that Charlie had had good treatment. 'This seems to be much more an issue of bureaucracy, inertia and arrogance.'

He said Charlie's parents are coping 'amazingly'.

'Given the stress they are under, the grace in these horrid times has been superb. In my day job I work with people who choose to be in the public eye. These people don't. They have been superb. I can't imagine what they are going through.'

The judge requested proof that the hospital measurements of Charlie's head size are wrong and ordered his head be measured today. The head size is important because it is an indicator of brain development which indicates how much damage might or might not have been done already by the illness.

The family's lawyer told the court that leading scientists' evidence supports those doctors who believe he could be helped in the US.

The judge is not expected to reach a decision today.

Dozens of 'Charlie's Army' supporters were outside the High Court this morning.  #JeSuisCharlieGard trended on Twitter and passing car drivers tooted horns in support.

The family also has the backing of Americans United for Life, the pro-life law firm, which has posted a petition calling for him to be allowed a final chance and already signed by nearly half a million people. 

AUL's president, the influential lawyer Catherine Glenn Foster, has flown to the UK and is in court, tweeting the proceedings, along with a photograph of herself comforting baby Charlie with a kiss in hospital.

She also tweeted an explanation for the parents' walk-out:

US evangelical pastor Rev Patrick Mahoney, a prominent pro-life campaigner has also flown in from Washington to pray with the family. In 1992, Mahoney was sentenced to six months prison, along with three others, for breaching a restraining order prohibiting them from protesting in front of abortion clinics.

He was initially barred from praying at Charlie's bedside at Great Ormond Street but the ban was rescinded.

He has also been posting from Court 50 at the High Court, on Facebook.

The AUL petition reads: 'We just heard about a breakthrough in the fight for Charlie's life! The Great Ormond Street hospital is requesting a re-hearing with the High Court. The preliminary hearing will take place on Monday, July 9th. The hearing will likely continue on Thursday. This is a sign that the hospital is finally recognizing that Charlie deserves a chance at receiving treatment in accordance with his parents' wishes.

'Thank you for your efforts on behalf of Charlie! Please sign this petition and share it with your friends. We must maintain momentum on this campaign!'

Foster is aiming for a million signatures.

Ahead of the hearing, Chris and Connie said: 'We are continuing to spend every moment, working around the clock to save our dear baby Charlie. We've been requesting this specialized treatment since November, and never asked the hospital, Courts or anyone for anything – except for the permission to go.

'We've raised over £1.2 Million and have had invitations from specialized Doctors in the U.S. and Italy offer their ground-breaking treatment to us and are confident they can help little Charlie. We will continue to make the case for us to seek treatment for Charlie with Doctors that are actually specialized in Mitochondrial DNA depletion syndrome and we hope the Judge and the Courts will finally rule in favor of us seeking treatment elsewhere. We love him more than life itself. If he's still fighting, then we're still fighting.'

Catherine Glenn Foster said:  'The medical evidence is consistently clear that Charlie deserves a chance at life. There is much misinformation about Charlie's condition but he shows no signs of being in pain and experts say that alternative treatment has a chance of improving Charlie's quality of life.

'It is unacceptable that Charlie's parents are being asked to prove that their son's life is still worth fighting for when it is their right as parents to pursue what they consider best for Charlie.

'We have letters and invitations from Doctors and specialists from around the world and medical evidence that shows that Charlie could greatly benefit from this ground-breaking treatment. Charlie's parents have been seeking this treatment since November – it is now July – time is of the essence.'

Foster said there is growing medical and ethical support for Charlie to be given the opportunity to seek alternative treatment. 'Experts say that there is a up to 10 per cent, and around 90 –100 per cent chance the medicine will cross the blood brain barrier, this is relevant regarding (albeit unproven) claims of brain damage, and this is a chance that Charlie's parents and many doctors and specialists around the world are willing to take. All we're asking is that the Judge and the Court give Charlie this chance.'