Assange's lawyers argued to the court that the warrant, issued back in 2012, had lost it's objective.
Assange is still living in the Ecuadorian embassy, where he has resided for more than five years out of fear he is would be extradited to the USA for questioning over the activities of WikiLeaks.
Lawyers for Assange argued in a London courtroom that the outstanding British warrant, issued after Assange skipped bail, had "lost its goal and function" following Sweden's decision past year to drop an investigation into sexual assault allegations.
Assange's legal team is now arguing that British authorities should "stop pursuing him for breaching bail terms because it was not in the public interest". Though that case eventually timed out in May a year ago, the unwelcome guest has stayed put because he fears being arrested by British police and handed over to the Americans, who want to prosecute him over his WikiLeaks website. UK Judge Emma Arbuthnot ruled that the argument for discarding the warrant wan't persuasive enough.
Should she rule in Assange's favour next Tuesday, it remains unlikely however that he will leave the embassy immediately.
His lawyers have now made an application at Westminster Magistrates' Court last for the United Kingdom warrant to be withdrawn, saying it had "lost its objective and its function".
His supporters say his health has deteriorated significantly during his years in the embassy, and the London court heard he had suffered depression, dental and shoulder problems.
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He claimed being extradited to Sweden would see him removed to the U.S. over WikiLeaks' publication of war logs and diplomatic cables.
Representing Mr Assange, Mark Summers QC said: "This was at all stages an investigatory European Arrest Warrant in respect of which there never were any underlying charges, where Mr Assange left Sweden lawfully in 2010 having been interviewed with the permission of the prosecutors".
But Crown Prosecution Service lawyer Aaron Watkins told the court it would be "absurd" if a defendant was effectively rewarded for managing to evade proceedings for sufficiently long that they fell away.
For the time being, Assange is free from arrest so long as he stays inside the embassy of Ecuador, which has granted him political asylum. "Mr Assange failed to surrender to custody".
This meant bail warrant was the only thing keeping Assange in the embassy.
Assange's defenders call him a freedom fighter who's being persecuted for telling the truth.
The British government has already refused a request for Mr Assange to be bestowed diplomatic status granting immunity should he try to leave the building.