This is the fabric used to make The Doctor’s waistcoat as seen in The Day Of The Doctor.
These images are directly scanned from fabric that was part of the bolt that was cut to make Matt’s screen-worn waistcoat. I’ve colour-matched them to the material, erring on the side of a bit brighter to show detail.
The fabric is woven in a twill, creating a fine Prince Of Wales style check.
Here’s the fabric in close detail.
The book classes the pattern as a Glenurquhart check.
It describes it as a twill weave in dark and light coloured warp and weft, creating the check effect.