No, the US does not recognize the notion of diplomatic asylum, nor does Britain.
The US has granted political asylum to people, but only when they were on US soil.
Julian didn't run.
You two are on a first-name basis...?
In fact, Assange did run: he had an interview with the police and prosecutors scheduled in Sweden for September 28th. He left the country on September 27th. When the authorities informed his lawyer that they planned to file a warrant for his arrest, they were told Assange would be back in Sweden by October 8th, and he'd be willing to meet with them then. He never showed up, at which point Sweden ordered him "arrested in absentia" and began the extradition process.
In fact, Assange's lawyer Hurtig was accused by the British High Court of deliberately trying to mislead the court over this sequence of events.
If you do something right once, someone will ask you to do it again.