District Judge Vanessa Baraitser said the 49-year-old Australian publisher faced 'oppressive' conditions in maximum-security isolation if detained in the US.
The hearing at the Central Criminal Court, the Old Bailey, is due to last three to four weeks. It had been due to go ahead in April but was delayed due to the coronavirus outbreak.
Assange, 48, faces 18 counts in the US including conspiring to hack government computers and violating an espionage law. He could spend decades in prison if convicted.
The 47-year-old was due to appear in a London court later Friday via video link, as he sought to avoid being forcibly taken to the US.
The 47-year-old Australian is currently serving a 50-week prison sentence for violating bail conditions in 2012 when he was wanted on accusations of sexual assault in Sweden.
The United States has requested the extradition of Assange, who was dragged from the Ecuadorean embassy in London on 11 April.
Magistrate Karen Martinez ruled that the suit could not move forward, as filed by WikiLeaks' attorney, the former Spanish judge Baltasar Garzon.
Neither the UK’s Foreign and Commonwealth Office nor lawyers for Assange immediately responded to emails seeking comment after normal business hours.
Assange, 46, fled to the embassy in June 2012 after skipping bail to avoid being sent to Sweden to face an allegation of rape, which he denied.
Julian Assange, 46, fled to the embassy in the wealthy Knightsbridge district of the British capital in 2012 after skipping bail.
Wearing a leather jacket and with his fist in the air, Assange described the decision as a victory.
Assange, who has repeatedly denied the rape allegation, sought refuge in Ecuador’s embassy in August 2012.
A UN panel has ruled The WikiLeaks founder should be allowed to go free from the Ecuadorian embassy.
Julian Assange says he will leave London where he took refuge, if a UN panel rules against him.
The 43-year-old Australian has been stuck inside Ecuador’s London embassy since June 2012.
Julian Assange has spent over two years in the Ecuadorian Embassy in London.
The Wikileaks founder says he will leave the Ecuadorian Embassy "soon".
The WikiLeaks founder says people need to take more responsibility for what they share on the internet.
