Dublin Instead of London Becomes The Center of Power in The Islands of NW Europe
Picture this:
1014 AD, the Battle of Clontarf goes differently. It's a crushing victory for Sigtrygg Silkbeard, who proceeds to take control of most of Ireland. By his death in 1042, his realm dominates the island, and most lands not under his direct control are held by vassals and client kings.
Also in 1042, Edward the Confessor becomes King of England. His death in 1066 sparks the 3-way contest between Harold Hardrada, Harold Godwinson, and William of Normandy that it did in our history. But Harold Hardrada wins the Battle of Stamford Bridge, killing Harold Godwinson, and swiftly takes control of the north of England. William's landing at Pevensey is uncontested, and much of the nobility of southern England rallies to him. He suppresses the remainder, and by October marches north to face Harold. But poor weather and inconclusive skirmishes prevent a real reckoning, and the two monarchs never actually come to a decisive battle.
The border between them develops along similar lines to the Danelaw, and local chieftains in Wales, Scotland, and Cornwall successfully play both sides to the point that neither can get a persistent advantage over the other. These local chiefs are aided by the Irish Sigtrygg dynasty, which deliberately keeps England destabilized to ensure its own mastery of the Irish Sea.
Britain develops as a battleground between Norway, Ireland, and the rising power of metropolitan France, and never winds up being united under a single native crown.