Baby talk after alleged Julian Assange rape

A woman who claims she was raped by Julian Assange joked about being pregnant and what they would name the baby shortly after the alleged offence, a court has been told.

The WikiLeaks founder on Tuesday began a High Court challenge against an extradition order that would see him taken to Stockholm to face allegations of sexual assault and rape against two women in August 2010.

In February Assange, now 40, was ordered to return to Sweden by senior district judge Howard Riddle, who dismissed claims by the Australian's legal team that the extradition was without legal basis and would result in a violation of his human rights.

However the European Arrest Warrant issued by Swedish authorities and submitted to Judge Riddle, is not "a fair and accurate description of the circumstances", Ben Emmerson, QC, acting for Assange, argued on Tuesday.

Subsequently, Mr Emmerson said Judge Riddle "got it wrong" in his decision to extradite Assange.

February's hearing was told by prosecutors that Assange's actions were violent and forceful at times and that he had unprotected sex with one of the complainants against her wishes.

However Mr Emmerson said that on all occasions sex with the women was consensual and that under British law, contained no elements of criminality.

While he has not been charged with any offence, the claims against Assange include three counts of sexual assault and one of rape.

With respect to the latter claim it is alleged that after a night of consensual sex, the pair slept before the woman woke to find Assange having unprotected intercourse with her.

"She immediately asked: 'Are you wearing anything?' and he answered 'You'," Mr Emmerson told the court, referring to court documents.

"She told him 'You better don't (sic) have HIV' and he answered 'Of course not'. She felt it was too late. He was already inside her and she let him continue."

After sex, Mr Emmerson said the woman joked about the prospect of becoming pregnant, telling Assange that he would have to pay her student loans.

"They joked about what they would call the child," Mr Emmerson said.

Mark Summers, also acting for Assange, argued that the warrant issued is legally non-compliant.

"It is a requirement that the person who is the subject of an arrest warrant is an accused," Mr Summers said, adding that Assange is not named as such.

Furthermore, he said Swedish prosecutors have not granted access to "the whole dossier" of evidence in the Assange investigation.

"As a matter of law in Sweden, the timing and access of the dossier is directly linked to the decision to prosecute," he said.

"This case remains at the stage where a prosecutor is yet to make the decision whether a prosecution will be commenced."

Dressed in a suit and wearing spectacles, Assange listened closely to Tuesday's arguments and as he left court refrained from his typically verbose speech to waiting media.

While his case is ongoing, Assange is on bail, wearing an electronic tracking device and reporting to police.

The appeal continues on Wednesday.

- AAP