A judge, who allowed a trio charged with terror offences to walk free, had recently liked a social media post branding Israel a "terrorist" and calling for a "free Palestine".
Senior deputy district judge Tan Ikram "decided not to punish" three women who displayed parachute images at a pro-Palestine protest.
But just three weeks ago, the judge liked a LinkedIn post published by a barrister who had promoted conspiracy theories claiming that Israel allowed the October 7 attack.
Ikram could now see disciplinary action after judicial guidance issued last year said judges known to have strong views should consider whether to hear a case.
A judge, who allowed a trio charged with terror offences to walk free, had recently liked a social media post branding Israel a 'terrorist' and calling for a 'free Palestine'Getty/ XA review of the sentencing has now been called on by legal figures including a former home secretary and a Jewish campaign group.
The case has been referred to the Attorney General, Downing Street has said.
"Serious questions are being raised in government on how a judge posting this online was able to preside over this landmark case and what this means for the sentencing decision," a source told The Times.
Heba Alhayek, Pauline Ankunda and Noimutu Olayinka Taiwo were found guilty of an offence under the Terrorism Act on Tuesday.
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The women displayed pictures of paragliders at a protest in London following the October attack by Hamas on Israel.
Militants from Hamas used paragliders to enter Israel from Gaza before killing more than 1,000 Israelis.
They were each given a 12-month conditional discharge, which means they could face a prison sentence if they carry out another crime within the year.
Lord Wolfson KC, former justice minister, said: "Of course judges, like the rest of us, have political opinions. But the longstanding practice of the judiciary was to keep those opinions private, at least for so long as the judge continued to sit.
Heba Alhayek, Pauline Ankunda and Noimutu Olayinka Taiwo were found guilty of an offence under the Terrorism Act on Tuesday
PA
"In an age of social media, where it is so easy to ‘like’ politically controversial posts, that practice seems all the wiser, both to ensure that justice is done, and also — which is as important — that justice is seen to be done."
Suella Braverman, former home secretary added: "I am shocked and deeply concerned at these findings. We must have confidence that judges are impartial and act in the interests of justice at all times.
"This raises serious questions about the sentencing of these despicable criminals and there must be an immediate review."
On behalf of Ikram, a spokeswoman for the Judicial Office press office said: "I didn’t know that I’d liked that post. If I did then it was a genuine mistake."