The former English Defence League (EDL) leader, 35, was freed from prison last month after three leading judges quashed a contempt of court finding made at Leeds Crown Court.
But he could be sent back to jail if he is again found in contempt for filming people in a criminal trial in Leeds and broadcasting the footage on social media.
Following a brief hearing of the contempt case at the Old Bailey today, a video appearing to show Robinson at a window within the court building was posted on the Twitter account of Ezra Levant, a reporter for the right-wing Rebel Media organisation.
In the footage Robinson says "that's such a good feeling" before promising to go and greet the crowd of hundreds of supporters cheering and chanting outside.
The video is believed to have been made in the canteen on the Old Bailey's second floor. By Thursday afternoon it had been viewed more than 160,000 times.
Section 41 of the Criminal Justice Act 1925 (CJA 1925) makes it an offence to photograph people within court precincts.
A City of London Police spokesman said: "We have been made aware of a video on social media which appears to show filming taking place inside the Central Criminal Court, and has been shared online.
"We will be looking into whether any offences have been committed."
Robinson was earlier ushered into court amid a large police presence as supporters, holding Union and St George's flags, chanted his name, while photographers and camera operators jostled for position.
In a Facebook live video earlier on Thursday morning Robinson said "this trial is a crock of s***" but asked if he was feeling confident, he told the Press Association: "Yeah, quietly."
He was referred to by his real name, Stephen Yaxley-Lennon, throughout a brief hearing, during which he sat behind his barrister Richard Furlong in the courtroom, wearing jeans, black trainers, and a grey checked jacket.
The Recorder of London, Judge Nicholas Hilliard QC, adjourned the case, saying he would receive written submissions before making a ruling at a later date on whether the contempt of court hearing will take place at the Old Bailey.
Robinson was released from prison last month and granted conditional bail from a 13-month jail-term.
He has already served the equivalent of four months in prison, but if found to be in contempt of court again could be sent back to jail - the maximum sentence is two years.
Speaking to reporters outside court, Robinson criticised the justice system, saying the case had already faced several delays.
"I believe they want me in prison for Christmas," he said.
"The law's supposed to be blind, but it's not supposed to be deaf and dumb. I'm being specifically targeted for who I am.
"I want closure. I believe they are purposely not giving me closure.
"We are in the Old Bailey, the highest court in the land. The rest of the people here are on trial for terrorism and murder.
"I'm on trial for speaking into a microphone."
Robinson was mobbed by supporters as he left court, causing traffic to be stopped as he posed for selfies and chatted with fans.
Among his entourage was Gavin McInnes, co-founder of Vice and the "Western chauvinist" group Proud Boys.
Some among the crowd directed their anger at the media, verbally abusing photographers.
One woman was filmed pushing a photographer as she called him "racist" and "Christianophobic".
Robinson was sentenced in May to 10 months' imprisonment for contempt of court in Leeds, which he admitted, and a further three months for breaching a previous suspended sentence.
In May last year he faced contempt proceedings over footage he filmed during the trial of four men who were later convicted of gang-raping a teenage girl.
A judge at Canterbury Crown Court gave him a three-month suspended sentence and told him his punishment was not about "freedom of speech or freedom of the press" but about "justice and ensuring that a trial can be carried out justly and fairly".
Robinson appealed against both contempt findings at a hearing last month heard by Lord Chief Justice Lord Burnett, Mr Justice Turner and Mrs Justice McGowan.
They found the judge in Leeds should not have commenced contempt proceedings that day.
Lord Burnett said "no particulars of the contempt were formulated or put to the appellant", and there was "a muddle over the nature of the contempt being considered".
He added: "Where a custodial term of considerable length is being imposed, it should not usually occur so quickly after the conduct which is complained of; a sentence of committal to immediate custody had been pronounced within five hours of the conduct taking place."
The judges dismissed Robinson's appeal in respect of the contempt finding at Canterbury Crown Court.