Judges are considering an attempt by English Defence League (EDL) founder Tommy Robinson to be freed from prison.
The far-right leader, who is appearing under his real name of Stephen Christopher Yaxley-Lennon, was jailed in May after he broke blanket reporting restrictions on an ongoing set of trials by discussing them in a Facebook Live video.
A judge at Leeds Crown Court said Robinson admitted contempt of court and jailed him for a total of 13 months.
But his barrister told the Court of Appeal Robinson should be freed from prison and have his sentence "quashed" after arguing that criminal procedure rules had been broken.
Jeremy Dein QC argued that a judge at Leeds Crown Court should have adjourned the case to give Robinson further time with lawyers, and to respond to each allegation in detail, rather than jailing him within hours of the video being broadcast.
He also argued that the 13-month sentence handed down was "manifestly excessive" and may have been lower if a barrister was able to properly mitigate on his behalf.
The Lord Chief Justice said he and two other judges would consider the submissions and hope to come to a judgement by the end of July.
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Robinson was previously spared jail after committing contempt in another case in Canterbury in 2017, on the condition he committed no further crimes.
Judge Geoffrey Marson QC activated that three-month term and added 10 months for the new offence, telling Robinson that he risked causing a trial to collapse.
Protesters gathered outside the Royal Courts of Justice in London ahead of the hearing on Wednesday, which was before the Lord Chief Justice of England and Wales, the Rt Hon Sir Ian Burnett, Mr Justice Turner and Mrs Justice McGowan DBE.
They may choose to reserve judgement to a later date after hearing evidence.
It comes a day after reports that lobbying by the far-right Breitbart news website caused the US ambassador for international religious freedom to raise Robinson's case with the British government.
US Senator Sam Brownback reportedly told British ambassador Sir Kim Darroch the UK should be more “sympathetic” to the former leader of the EDL and warned Sir Kim that the Trump administration might publicly criticise its handling of the case.
Robinson has been forming links with the American alt-right, who characterise him as a “citizen journalist” and see imprisonment as a violation of freedom of speech.
Steve Bannon, the former Breitbart chairman who served as the White House chief strategist, has given his personal support to Robinson and former Breitbart London editor Raheem Kassam has coordinated two “Free Tommy” rallies.
A neoconservative US think-tank said it was funding both Robinson's legal costs and two protests in London on 9 June and 14 July.
The June protest saw Robinson supporters perform Nazi salutes and attack police, while Saturday's event - which merged with a pro-Trump march - saw demonstrators blockade a bus driven by a Muslim woman and several arrests.
MPs and campaigners warned that far-right extremists were rallying around his imprisonment to develop a new “racist street movement” with international support.
It comes as statistics show more extreme right-wing terrorists are being arrested and jailed than ever before, with the head of MI5 warning that their brand of extremism was “rearing its ugly head” once more.
Prosecutors and police said Robinson’s posts radicalised Darren Osborne, the terrorist who ploughed a van into a group of Muslim worshippers in Finsbury Park last year.
Good morning and welcome to our live blog on a challenge against Tommy Robinson's 13-month prison sentence at the Court of Appeal. The EDL founder, whose real name is Stephen Christopher Yaxley-Lennon, admitted committing contempt of court by broadcasting a Facebook Live video that discussed a trial subject to blanket reporting restrictions in Leeds.
The footage, which was broadcast for more than an hour, was watched 250,000 times within hours of being posted on Facebook after Robinson urged followers to share it.
The far-right activist was given 10 months for contempt of court, and a further three months for breaching a previous suspended sentence for the same crime in Canterbury.
The hearing was due to start at 10.30am but has been delayed. There is a small group of Free Tommy supporters outside the Royal Courts of Justice, where police are stationed.
The courtroom itself is packed, and Robinson is appearing via video link from prison.
The feed shows him sitting in a dark shirt as he waits for proceedings to start.
The court is now in session, and Robinson has confirmed his real name Stephen Yaxley-Lennon.
The Lord Chief Justice says "it's heartening to see so many people who are interested in the case in court" and appeals for them not to disrupt the case.
"We must remember that there remains in place an order in the Leeds Crown Court prohibiting reporting of what has occured at two trials."
He confirms that there is no application for these proceedings to be subject to reporting restrictions.
A judge at Leeds cCrown Court initially banned reporting of contempt proceedings against Lennon but it was overturned following a challenge from The Independent and local media
Robinson's representatives are appealing for the court to overturn sentences handed to Robinson at Canterbury and Leeds.
His barrister says they were both "out of time".
"It has become evident that there is a chequered background as far as both proceedings are concerned."
They are applying for the court to extend the time allowed for appeal because communication was "extremely difficult" with Robinson due to him being held in what they argue to be effectively solitary confinement.
Robinson's barrister says after he was transferred from HMP Hull to Onley prison an appointment was cancelled and a meeting was delayed, then they found parts of court transcripts from Leeds were missing.
Solicitors visited Robinson on 21 June and say a conference scheduled for two hours only lasted for 55 minutes because it took officers 1 hr and a quarter to bring the prisoner out.
"Access to him has been difficult to say the least."
Robinson's barrister says: "The defendant was subject to what we contend were solitary confinement conditions and he has extremely limited access to telephones and it wasn't straightforward by any means for communication to unfold."
He says they could not submit grounds for the appeal until 12 July because of the above delays.
A judge points out that the delays apply to the Leeds case, but not Robinson's previous sentence for contempt at Canterbury Crown Court in 2017.
"He did not know that anything in those proceedings was deficient," the barrister replies.