On the underside of the 11th Doctor’s “scales” waistcoat was a front facing, made of self (“scales”) fabric.
This facing wasn’t “grown on” (cut on); it was, rather, a separate piece, as indicated by the seam line running down the center front.
It’s not clear exactly how far the front facing extended, but it was at least past the lower corners.
Alex Murphy (aka “The Ginger Doctor”) and Daniel Pawlik also claim the original costumer told them that the waistcoats were underlined (“flatlined”) with lightweight hair canvas.
You can read his original blog post here:
https://thegingerdoctor.wordpress.com/2017/04/01/tipping-the-scales-eleventh-doctor-nirvana/
The waistcoat was lined with white (or, perhaps more likely, off-white) fabric – perhaps something as simple as a lightweight cotton or muslin.
This was most commonly observable over the back of the neck.
If you look closely, you’ll also see a center back seam in the lining.
The lining didn’t appear to be understitched around the armscye; it frequently “poked out” from underneath the back arm hole.
The lining didn’t appear to extend downward to the lower front edge of the waistcoat (nor would one expect it to do so).
However, the lining did appear to extend to the lower back of the waistcoat.