Below is a map of the British Isles with 15 locations marked (the yellow circles) where our Bakers most likely originated or lived long enough to pick up/leave a DNA imprint. While it is generally agreed that “Baker” was originally an English surname, it is also true that they quickly spread out through Scotland, Ireland, and Wales (not to mention later to Australia and America), so that Bakers from these areas have long been common occurrences. (This map is part of the “Genetic Communities” information provided by Ancestry as the results of my own a-DNA testing.)

See the map with both overlays here.
(Click on the map below to see it at full size, so you can read the smaller print.)