By Abe Maddison, Dominic Giannini in Canberra

Granting Julian Assange leave to appeal his extradition is a “huge blow” to a US case to extradite him from the UK and one that could be insurmountable, his Australian-based lawyer says.

Jennifer Robinson, who has represented Assange since 2010, said the British High Court’s decision was a major relief for Assange and his family but it could be months before the new appeal is heard.

“It’s only a temporary reprieve, he’s still at risk of extradition and that’s something that everybody needs to realise,” she said on Tuesday.

“We haven’t won yet. This is just one step along a very, very long road.”

The judges accepted there was an arguable case Assange could be discriminated against, after being told a US prosecutor had said the First Amendment may not apply to foreigners when it came to national security.

“So the key question now is will he, as an Australian citizen and national and journalist and publisher, be entitled to the First Amendment, or will he be discriminated against on the grounds of his nationality,” Ms Robinson said.

“We say he will be and that that cannot be remedied.”

The US was in a difficult legal position, Ms Robinson said, with Assange’s team given permission to lodge a fresh appeal.

“It’s a huge blow to their case and one that could be insurmountable,” she said.

The Australian government has lobbied the US administration to bring its case to an end.

“By allowing this appeal process to continue, they’re only keeping him in prison for longer when he’s already spent five-and-a-half years unjustly detained in a high-security prison because of this extradition request,” Ms Robinson said.

“It’s really time for the US to drop it and let this end.”

Prime Minister Anthony Albanese said his government would continue to work in a “constructive fashion” and maintained its position the pursuit of Assange had gone on long enough.

“There’s nothing to be served by the ongoing incarceration of Mr Assange and we continue to work very closely to achieve that outcome,” he told reporters in Sydney.

Assange, 52, is wanted in the US on 18 charges, nearly all under the Espionage Act, relating to WikiLeaks’ mass release of secret US documents – the largest security breach of its kind in US military history.

Ms Robinson said the appeal process had been “incredibly complicated” and taken a toll on Assange, who did not appear in court because of concerns for his health, and his family.

“Just last night, as the court was deliberating on the decision, I was in contact with Stella, his wife,” she said.

“For her to be sitting in court not knowing whether her husband and the father of her children may well be put on a plane to prison conditions that will cause his death is a terrifying prospect for any family.

“It’s a really disappointing reflection of how the legal system can be weaponised and I call it punishment by process. He has been tied up in all kinds of legal different legal processes for the past 14 years that have restricted his liberty without conviction.”

The Wikileaks founder’s brother, Gabriel Shipton, said it was “quite embarrassing” for the US Department of Justice and the State Department to have one of their assurances rejected by the court.

“It will feed back into Washington, where just last month Joe Biden said he was actually considering the Australian request to drop the charges entirely,” he told the ABC.

“This all adds into the political cost around this prosecution. It’s all adding up now.”

Ms Robinson was “very encouraged” by President Biden’s comments saying he was considering dropping the case.

“It goes to show the Australian government is raising this … at the highest levels for the president to respond to a question like that in public,” she said.