Adobe Analytics offers Cities and Councils for the UK, and Cities, US States, and US DMA region for the United States. There is currently no UK region as you're describing, nor have I heard plans to introduce it.
You could create an idea thread here in the forums and let the community vote on it.
Sadly the region breakdown is a bit of a misnomer...
Think of region as being more of a state or province segmentation.
I havent tried this specifically but what if you made a saint classification for each concerned city "new region".
It may work where you can then report on sub classification "new region" instead of city
North East England, City 1
North East England, City 2
North East England, City 3
South East England, City 4
East Midlands, City 5
Now the "new region" report would then be broken into the proper district you define. it would be a bit of work at first but then once done its automatic. Then you can pull report or segment by "new region" sub classifications.