Assange entered the embassy in 2012 to dodge a European arrest warrant issued over a Swedish probe into rape allegations, but Stockholm dropped its investigation last year.
However, British police say they will still arrest Assange if he steps foot outside the embassy for failing to surrender to a court after violating bail terms.
Assange's lawyer Mark Summers told a London court that the warrant had "lost its purpose and its function".
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Summers said Assange had "spent five and a half years in conditions which, on any view, are akin to imprisonment, without access to adequate medical care or sunlight, in circumstances where his physical and psychological health have deteriorated and are in serious peril".
The court heard that Assange was suffering from a bad tooth, a frozen shoulder and depression.
Prosecutor Aaron Watkins called the court bid "absurd".
"The proper approach is that when a discrete, standalone offence of failing to surrender occurs, it always remains open to this court to secure the arrest," he added.
Ecuador earlier this month granted citizenship to Assange, who fears that, if he leaves, he will be extradited to the United States over WikiLeaks' publication of leaked secret US military documents and diplomatic cables in 2010.
Ecuador also asked London to recognise Assange as a diplomat - which would give him safe passage out of the embassy without fear of arrest - but Britain refused.
Sweden dropped their investigation over the 2010 allegations last year.
The prosecution said it was expecting a judgement on February 6.
