The people who settled northern England were by and large not Saxons but Angles. Essex, Wessex and Sussex were all "Saxon" (see /u/alriclofgar's answer below) kingdoms, their names deriving from the various tribes who they claim founded them. Wessex, for example, was Westseaxna Rīce, or the Kingdom of the West Saxons. There were Middle Saxons, but they never managed to found a lasting kingdom. Nevertheless, the region they controlled gave name to Middlesex.

The "Angles" also founded a number of kingdoms, the most notable being East Anglia, Northumbria and Mercia. The etymology of East Anglia is obvious enough, and Northumbria was named as such because it was north of the Humber, a river/estuary in northern England. Mercia is somewhat trickier but derives from the Old English Mierce or Myrce, meaning "border people", from the Old English mearc. It's from mearc that we also get the modern English word "march" It is cognate with the modern English word "march", in the sense of border - for example the Welsh and Scottish marches (i.e. the lands on the English-Welsh and English-Scottish borders), but that's beside the point.

What I'm getting at is the Kingdom of Mercia would have been the likely candidates for "Norsex", except they were of Angle descent and therefore would not have been considered North Saxons in the first place.

EDIT: Made some changes to fit better with what /u/alriclofgar pointed out.