Ecuador offered this, saying they are welcome to question him in their embassy but the Swedes refused. It's blatantly obvious the US is leaning very hard on both the UK and SE.
There are a number of legitimate reasons Sweden would refuse this idea. Foremost among them is that, in the event this questioning leads to a decision to arrest, it likely can't be performed.
http://www.dailymail.co.uk/news/article-184038/Police-smash-...
http://www.sussex.police.uk/about-us/policies-and-procedures...
(UK has around 40 regional police forces along with various national agencies.)
Unusual yes, but not unheard of.
As a personal anecdote, there is a close friend of my family who has been facing extradition to another country merely for questioning over something that he allegedly did in 1944.
Seems very similar.
Not sure it applies here, though.
There is still something very funny about this insistence that the questioning happens in Sweden. Swedish police can come to UK to question. UK police could question on behalf of Swedish police, there are arrangements for that I think.
Extradition when there are no charges is unusual.
The UK have been here before, General Pinochet and the Spanish judges spring to mind.
Edit: further reading on European arrest warrants makes me realise that each country in Europe has a different definition of 'arrest'.