Lawyers for WikiLeaks founder Julian Assange look set to fight on to stop his extradition to Sweden where he faces sex crime allegations.
The Supreme Court decided by a 5-2 majority that extradition was lawful and could go ahead.
But Dinah Rose QC immediately told the country's highest court that Assange was considering an application for his case to be reopened on the basis that there had been a flawed hearing. Assange, 40, was given 14 days to consider the judgment before making a final decision on his next move.
The Swedish authorities want him to answer accusations of raping one woman and sexually molesting and coercing another in Stockholm in August 2010 while on a visit to give a lecture.
Assange, whose WikiLeaks website has published a mass of leaked diplomatic cables that embarrassed several governments and international businesses, says the sex was consensual and the allegations against him are politically motivated.
The majority of Supreme Court justices rejected Assange's argument that the European arrest warrant (EAW) issued against him by Sweden was "invalid and unenforceable". Ms Rose contended that the Swedish public prosecutor who issued the EAW was not a "judicial authority". Warrants could not be issued by prosecutors but only by a court, judge or magistrate.
After her argument was rejected, Ms Rose gave her warning that an application could now be made "to reopen the argument" before the justices. Ms Rose said there was "concern" that the court majority had based their decision on an interpretation of the Vienna Convention on the Law of Treaties she had had no opportunity to address.
Lord Phillips, court president, said the point of law which had to be considered had not been simple to resolve. He gave Assange's legal team 14 days to consider the court's ruling before deciding whether to press for a further hearing.
Solicitor Gareth Peirce, who represents Assange, said after the hearing: "We are going to ask the Supreme Court to reconsider." She said the case had raised an important legal issue about the meaning of "judicial authority". She suggested that MPs had thought that a judicial authority meant a judge rather than a prosecutor when they adopted extradition rules.
Journalist John Pilger, who was at the hearing to support Assange, said lawyers might also launch a challenge in a European court. "It's not over," he said. "It could come back here for a hearing. It could go to Europe - or both."