Scandinavia remains pagan throughout 10th and 11th century.
Scandinavian Crusade in the 1110s sees Norway and Western Sweden being granted to the King of England. Crusaders are given control of Denmark and Sweden, which are made into several principalities.
Christians from England, Normandy, and even some other locations are settled in Scandinavia, both in English Norway and in the principalities.
By the mid 1200s, the dialects of Scandinavia are very foreign-influenced. The ones in Norway are somewhat Anglicized.
In the 1300s, the King of England inherits a consolidated Denmark, and ten years later a consolidated Sweden. Holstein is conquered in a war that may also see the loss of a longer-held Normandy.
In the 1400s an English Civil War leads to a third of England's nobles relocating to Scandinavia, moving the capital to Copenhagen or Aarhus.
Stuff happens.
In the 1800s the dialect of English spoken in the British Empire and a former English colony in the Americas (both are geographically advantaged and are capable of rising in another TL) both begin to influence the Kingdom of Scandinavia/Denmark.
In the 1900s ATL America becomes the center of global culture and Scandinavian becomes more English/American influenced.
In the late 1900s, a world war unites Scandinavia with the British, whose colonies are failing. That, or an inheritance simply happens, and because of good relations between nations and fairly similar systems of governance, and maybe a large Russia, Germany, or Turkish Empire, people decide to go along with it instead of just establishing a republic in one of the nations. Or both.
By 2012, vernacular Scandinavian with all the newest globalized slang is as similar to TTL's English as OTL English is to Scots. The written version is significantly more Norse.