He is currently imprisoned pending a USA appeal (which they have stated, to the court, they will make); his lawyer told the court that he would submit an application for bail on Wednesday (and not to the court today).
Appeals are not a right in the UK and rarely granted. This is a highly political case, so it might get herd. I hope he goes free. Assange is a true Australian hero, even though his own government abandoned him.
Right; to be pedantic, he is being held in custody until such point that the High Court decide to grant leave to appeal.
I would be frankly _amazed_ if in this case the High Court doesn't allow an appeal. And I'd be surprised if the Supreme Court didn't too. It's such a high profile and politicised case that it's incredibly likely to be viewed to be in the public interest.