In Blender, first make sure you are using blender rendered (Do not use Cycles rendered)
Select your mesh in edit mode
Select all mesh faces
In UV Image editor, remove the mapped image (While in edit mode, all faces of that mesh are selected) by clicking the small “X” button near the image file name
Remap the faces again by selecting the proper image from the image selection drop down menu
Now, the problem is happening because Blender have mapped each different face on a different image (Properly sometime caused by using “Ctrl-C” and “Ctrl-V”, use “Shift-D” next time to properly duplicate objects) so that it thinks, the whole mesh have some faces that are mapped on one texture, other faces on another and so on, in this case of OP it’s 7
When you import to Unity, it will also detect the same, so you can apply those 7 images onto that mesh!
Now, in some cases this is useful, but not in OP case!
If you don’t need to preserve your UVs, here’s a simpler solution: in blender, go to edit mode, press U. Choose “reset.” This does what Shbli says, just simpler. Hope this helps someone.