He did not run to the UK. The charges in Sweden had been dropped and he was allowed to leave the country. I'll give you that the UK is a bad choice to go, but at the time he was free and clear of any charges. Only after he was in the UK, Sweden reopened their investigation, and at first reported him as a "witness" they'd like to interview, and that's what they based their request for extradition on. He wasn't "accused" at the time Sweden filed.
His "pre-text" wasn't that he feared the UK would extradite him to the US, but that the UK would extradite him to Sweden, which would extradite him to the UK. So he was fearful of Sweden, not the UK. You can say that this is stupid or even claim he cannot genuinely believe that and is therefore disingenuous, but unless a true mindreader shows up, we cannot know what he thought and feared, really.