His Wikipedia entry is here and a site run by his family is here. The latter attempts to include all Fleetwood-Walker's works, major and minor.
As you will notice from the images below, he changed his style sometime around World War 2. Through the 1920s and 30s he painted crisply and smoothly, almost achieving an airbrushed look. Then he shifted to a much more casual style.
The subject is Marjory White, his first wife.
Thought to be the artist's wife and her younger sister.
From the appearance of the woman, I'd say that this depicts his own family.
Fleetwood-Walker painted several family portraits like these.
I think this Peggy was his second wife. By this time, he had dropped the hard-edge style for something more casual and painterly.
This is better drawn than some of his casual paintings. I have the feeling that Fleetwood-Walker had trouble placing eyes on faces (see the second link above and do some sub-linking for many examples of his work). But be aware that eye placement is not always easy, aside from full-face and profile views.