You need to go from Blender to UE, not the other way 
No need to look at the material shader in Blender, it’s irrelevant, it’s just the UVs that matter.
You need to get it so that the sections you’ve unwrapped, correspond to the correct part of the texture when it gets to UE.
So, this part, for instance
needs to be in the same place and size and the texture that is the side or your cork in the material, here
