Earlier this week, the UK government published a list of cases for the two-day hearing, which started on Tuesday. The court will decide whether Assange will have further opportunities to fight extradition to the United States before UK courts.
The demonstrators are holding up posters calling for Assange's release and his non-extradition to the US.
On Tuesday, several hundred people also held a rally in support of the jailed journalist in Paris, a Sputnik correspondent reported.
One of the last means of preventing his transfer to the US may be an appeal to the European Court of Human Rights. Assange lost his previous appeal at the UK High Court last June.
WikiLeaks was founded by Assange in 2006 but rose to prominence in 2010 when it began publishing large-scale leaks of classified government information, including from the US.