An important distinction needs to be made between the Viking raids which plagued all coastal regions starting in the late 8th century and the actual Viking invasions. The Great Heathen Army of Ivar the Boneless in 845 was the first major invasion of English territory. Quite possibly, that specific invasion would be butterflied away, but a full-scale Danish army landing somewhere in the mid-9th century is almost inevitable.
The Ragnarssons very neatly bumped off the Anglo-Saxon kingdoms one by one, starting with East Anglia, then advancing on stolen horses to Northumbria, which at the time was in the midst of civil war. As the richest and most powerful Anglo-Saxon kingdom, Northumbria was going to be the most appealing target.
To backtrack a little bit, I see Mercia moving into southern Northumbria and Strathclyde picking up the north. If Greater Mercia can avoid civil war and internal strife, they should have no trouble fighting off the Danes. Unfortunately, given the climate of the times, that's far from being a given.
If Mercia stays strong, the full fury of the Viking invasions will probably hit Strathclyde and the Saxon kingdoms instead.
The Saxon kingdoms will either be absorbed by Mercia, or, more interestingly, form a sort of British Normandy, perhaps even in union with Normandy in France.
If a Viking dynasty is seated in Strathclyde, a dynastic union with the Viking Lord of the Isles or the Jarls of Dublin or Man is possible too. I'd be intrigued to see a united Scotland and the North of England under a Norse dynasty.
Mercia may well wind up absorbing Wales as the OTL English did, as the Northern kingdom remains in the Scandinavian cultural and economic orbit and the Southern kingdom becomes associated with the Low Countries (as medieval southern England was)
