The "North East" is the proper name of a NUTS 1 [0] region of the UK. It is distinguished from your interpretation of it as the "north east of the UK" by its use of capital letters, as is standard in English [1].
It seems to be used both with and without.
In the main table with the maps it's not directly after, there's a comma. The ", England" is specifying the country, same as where it says "Yorkshire and the Humber, England", "East Midlands, England", etc. There's no comma part for "East of England", because there it is part of the name. In the demographics table it is directly followed by "England".