Horizontal white lines on display

I have a MacBook Pro (Retina, 13-inch, Mid 2014). Yesterday on the external monitor a thin bright white line appeared in the middle of the external monitor, in the middle of the screen and about 25% of the screen width. I assumed that this was a problem with the external monitor, but when I got home the white line had not only transferred to the MacBook screen, but another one further down had also appeared.

This morning when plugging in the external monitor both white lines have moved to the external monitor! See picture.

The weird thing is if I unplug the external display the lines move to the MacBook Retina display. The external display is connected to a thunderport and the problem happens with either port on the Mac.

Can't be the displays, so what is it? Anyone seen this before?