I would think so:
3 - Help & Support - Mobile Broadband Help - Got a question?
3 - Help & Support - International - 3 Like Home - Pay As You Go
But i'm not 100% sure, I don't have a 3 uk sim card. But it worked perfectly with my Italian card in both Sweden en Denmark.
btw: if you are going to use a lot of data: Three Sweden had a broadband offer for 99 krona for the sim card with 1 week included (at least they had last summer) and then you have unlimited broadband internet. They have something similar in Denmark and that one should even work in Sweden. The problem is that I wasn't able to buy one, because they wanted a Danish ID card.