Thank-you for such a specific link. It seems very clear. Except that the extradition treaty between the EU and the US makes no provision for refusing an extradition request because of any previous extradition. So I'm not clear why Sweden is making such a definite statement.
Confusingly https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/117679/european-arrest-warrant1.pdf does require that consent - but only for 45 days (article 28).
However Sweden has made a clear statement, so I'll concede that the judge was right to say that Assange wouldn't be further extradited without the agreement of the UK.