It really depends on how the vikings then tried to rule. You imply the vikings would have remained pagan even while ruling England, but the vikings often proved amenable to making practical choices if it eased the way for them to prosper. So I think it likely the viking leaders would have publicly converted to Christianity to reduce native resistance against them. Even if they didn't, they likely would have at least not acted against the Christians as it would probably incite widespread rebellion. They wouldn't necessarily have supported Christianity like previous English rulers, but they'd probably have tried to toe a line between submitting to the people and culture they conquered and doing what was necessary to hold their conquests. It's possible Norse immigrants would have established villages and ports that were largely pagan, but Norse paganism wasn't organized. Any real competition between Christianity, with dedicated monasteries and grand churches, and Norse paganism, which was humbler in nature and organized on a more local level, would almost certainly end up with Christianity becoming dominant. Unless the victories inspire a reorganization of Norse paganism to compete with the native Christian practices it's likely the pagans would convert over time to Christianity, nobles and commoners.
If the Norse did decide to try and convert England to their gods, it would almost certainly prove troublesome. If the vikings had eliminated all the local nobles in their conquests, there would be a lack of any organized rebellion or uprisings. However the people still would if the vikings basically went around burning parish churches, looting monasteries, destroying cathedrals, and overall forcing the people to choose between death and converting to their Norse gods. A strong enough Norse occupation force might still triumph, but the destruction and death would be widespread. Probably enough to cripple the population of England for generations, even if there was a constant influx of Norse settlers. During this time England would be threatened by the Welsh, Picts/Scots, and Britons.
Regardless of what route the Norse chose, if they successfully held onto England till their rule stabilized there would be major effects. Chances are that Wales, Scotland, and Ireland would almost certainly fall under Norse control. Norse trade ports like Dublin in Ireland were being settled around this period and lasted for a while. If a major Norse populace came into existence in England to supplement these viking expansion attempts before the natives really drove them off under the leadership of Brian Boru or Constantine II, I doubt the rest of Britain could resist. In turn Britain would enhance other viking activities. As long as this doesn't butterfly his existence or campaigns, Rollo's efforts in Normandy would be probably twice as fierce as there's a significant Norse population just across the channel to draw from. Eventually I figure the Norse would fall to civil war as kings like Cnut try to unify the Norse into a single kingdom. Either they succeed and we end up with a North Sea Empire-like Norse kingdom or the vikings descend into a multitude of small kingdoms and likely lose a great degree of influence in their lack of unity. Really depends on author's preference.