We call the region Μίντλαντς too (like Σίτι του Λονδίνου for the City).
Vicky's suggestion does not apply in this case as Ενδοχώρα or Μεσόγεια are used for inland and the Midlands are just that zone from east to west.
If you have to call it something in Greek, κεντρική Αγγλία would not be entirely wrong (though it means central England). If you wish to coin a word, I suggest Μεσοχώρα. But stick to Μίντλαντς if you want to be on the safe side. And if you need to translate Μεσόγεια (the region in Attica), go for Mesogeia.