If it helps, in 2008, a reconstructed viking boat took a bit over a month (29 June - 9 August) to sail from Roskilde to Dublin, via the Channel and round Cornwall. [(linky)(http://www.vikingeskibsmuseet.dk/en/the-sea-stallion-past-and-present/the-voyage-2008/)

Assuming a more experienced crew and a shorter voyage to the east coast rather than Dublin, you're probably looking at a week or two depending on wind and other factors - but there's probably proper sources to confirm/deny that.

It is a tricky question since those traveling didn't really record that sort of a thing. Check out my other post on distance and travel here. Of course this is based on trade ships, not necessarily longboats.

Brickie78's post is probably about right, anywhere from two to four weeks from Norway/Denmark to England.

I will see if I can dig up anything a bit more definitive, but this is all pretty much guesswork.

This is an interesting paper I found:

http://www.raunvis.hi.is/~thv/t_t.html

Has a quote from an Icelandic saga of the time

So the wise men say, that from Stadlandet in Norway there is seven days’ sailing to Horn in the East of Iceland, but from Snæfellsnes four days’ sailing to Cape Farewell in Greenland.

He makes the following conclusions

"The most important and the best substantiated of these data is the first point of the trip from Norway to Iceland, a stretch that was very frequently sailed. The distance in question is about 530 nautical miles so that the average time of 7 days corresponds to 76 miles per day or 3,2 knots on average. Such an average implies that single voyages might well have been twice as fast, thus taking only 3-4 days, say. All of this fits fairly well with information from other sources and also with modern experiments with replicas of Viking ships."

Great Britain is a pretty big place. Shetland Isles are quite close to Norway (200 km). To sail there, it would only be a voyage of 2 or 3 days for them.