Following their defeat, where did a significant number of Vikings establish settlements in Britain?

The Viking presence in Britain was more than just raids; they eventually established settlements, particularly in the east and north of England. This area came to be known as the Danelaw. Think of it as the "Dane-law," where the laws and customs of the Danes, who were a major group of Vikings, held sway. This happened from the late 9th century onwards, following significant Viking victories against the Anglo-Saxon kingdoms. The Danelaw wasn't just a geographical area; it was a distinct cultural and legal region with its own Viking-influenced laws and social structures. Places like York (then known as Jorvik) became major Viking centres. While Vikings certainly raided other parts of Britain, like Dorset and Lancashire, they didn't establish the same level of sustained control and legal framework as they did in the Danelaw. The Pale, on the other hand, refers to a region in Ireland under English control much later in history, so it has nothing to do with the Vikings.
Think of 'Dane-law' as the area where Viking laws and customs prevailed, marking their lasting presence on the British Isles.