The UK can send him to Sweden, saying they complied with EU rules. The UK can then relax, and not deal with the wrath of Australia being pissed off - an ex-commonwealth country.

Once he's convicted in Sweden, he can serve the two-months or whatever. Then he can be extradited to the US. Sweden can relax - he's a convicted sex offender now, extradited from the UK. It's harder for him to get legal support in Sweden - he's English-speaking, as are the majority of his supporters.

And the US gets their man. No government wants some renegade out there leaking their secrets.

The UK and US will obviously have discussed his extradition. They've agreed to try the Swedish route first. It doesn't have a political cost for the UK government.