If the longship departed from Stavanger, Norway, and landed at Newcastle on Tyne, England, the distance would be 350 nautical miles.
If the longship averaged 4 knots, the time would be 3 days 16 hours.
Obviously, this would vary depending on how much speed the wind and weather allowed the longship to make, and by the points of departure and landfall.
An accurate recreation of the Skuldelev 2 viking longboat, found in the Bay of Roskilde in Denmark actually took the trip a few years ago. It's one of the biggest ever found, so it would have been a fair bit faster than its contemporaries (the top speed reached in favourable winds was twelve knots).
Route can be seen here: http://www.vikingeskibsmuseet.dk/fagligt/skibenes-togter/tidligere-togter/havhingstens-togt-roskilde-irland-2007/
The crossing from Norway to the Orkneys took 50 hours, but half of that time she was being towed due to gale winds from the west. It's a distance of 294 miles across and with a very reasonable median speed of 6 knots in 10 m/s winds that would have taken 49 hours.
As a side info, the speed of a sailing boat can be inferred from its length and the wind speed and for a wind speed of 10 m/s (taken from the logs:http://www.vikingeskibsmuseet.dk/fagligt/skibenes-togter/tidligere-togter/havhingstens-togt-roskilde-irland-2007/logbog-dagboeger/alle/archive/2007/july/article/uddrag-fra-logbogen-tirsdag-den-17-og-onsdag-den-18-juli-2007/) and a length of ~30 metres, the speed would be ~6,8 knots.