An extradition is not a legal proceeding, it's a diplomatic one and being a democracy they can very well agree not to engage in a diplomatic exchange beforehand.
Well, I don't know what treaties are to the United Kingdom and Sweden, so I can't speak to the relevant matter, but there is a general sense (insofar as "international law" can be thought of as an actual concrete thing) that treaties are laws. To the United States, for example, treaties are explicitly treated as laws (see http://law.justia.com/constitution/us/article-2/18-treaties-...). Most other countries take their treaty obligations very seriously, although the actual mechanics depend on each country's legal/political system.
Source: http://sverigesradio.se/sida/artikel.aspx?programid=2054&art...