I know of no references to "north Germanic" in the 11th century. By that point the Anglo-Saxons were well established in England and had been for centuries, intermarrying with the locals and converted to Christianity. There were plenty of trade ties with the north Germans and there may have been a vague sense of common identity, but now you're getting into a question of ethnic identity, which just isn't really applicable to the time period ("gens" or race in Latin is a HUGE and contested subject).

And of course the Anglo-Saxons weren't the only game in town, as in the 11th century we're talking 200 years after the Danish conquest (and by Dane I mean Scandinavian) of much of Britain and the continued merging of Danish and AS peoples, as well as resistance to the Danes and the building of an "English" identity under such folks as King Alfred and his mythography.

Finally, in this period, England - indeed much of the North Sea - fell under Danish hegemony under the short-lived empire of Canute. Short lived as a political body, but not as a source for political legitimacy.

In short (too late) - no, I don't think there's any evidence to suggest that the Anglo-Saxon-Scandinavians of the 11th century thought of themselves as from north Germany, let alone had romantic feelings for same.

Follow up, you said 11th century, do you mean before or after the Norman conquest? If after, are you referring to the English of Saxon descent or the Normans? because both kinda have roots in northern Germany.

The English saw their Germanic cousins [retracted].