His most important performances for Scotland, and those which endeared him most to the Tartan Army, were against England at Wembley. In 1936, when trailing 1–0, Scotland were awarded a late penalty, which Walker volunteered to take.
In significant matches between Scotland and England at Wembley, Walker's performances were particularly notable. In 1936, after Scotland had fallen behind 1–0, they were awarded a late penalty, and Walker offered to take it.