The trip between southern Scandinavia and northern Britain would have taken 3-6 days in good conditions, although foul weather could delay departure or force travelers to run ahead of the storm far up the Norwegian coast.

The Viking Ship Museum in Roskilde, Denmark, did a trial run with a reconstructed longboat from Roskilde to Dublin in 2007. Roskilde lays in a fjord that leads into the actual Kattegat (which is the sea between Sweden and Denmark, not a town like in the TV show). It took three days to travel from Roskilde to Norway, another day or two sailing along the Norwegian coast, about 36 hours of open water from Bergen to the Orkneys, then a few days down the Scottish coast to get into the Irish Sea. It would take a similar amount of time to work down from the Orkneys to Northumbria. Because of the way the North Sea circulates, this is the most likely outbound route, although Scandinavians would have likely returned home by sailing the southern route down toward the Netherlands than along the west coast of Denmark. Travel times might also have been slowed by a need to travel as a fleet or convoy, probably with the fleet moving in stages and rallying at different points along the way before setting back out together.

You can see tracking from the 2007 voyage to Dublin here, and you might also want to check out the information from the return trip in 2008. There was a lot of documentary work done at the time, which means there's a good selection of YouTube videos now, based on how much time you want to spend watching. I'd recommend searching for the Sea Stallion of Glendalough (the name of the reconstructed ship; Glendalough is an area south of Dublin where the original ship's keel was likely laid, based upon tree rings in the surviving wood).

Wow! Thank you so much. You made my day. I'm actually from Sweden my self so I have a bit of knowledge about Norway and Denmark. Thanks again.