Although this is very pseudo military looking I don't think it is.
Women in organisations such as the Salvation or Church army wouldn't have dressed like this nor women in the military.
This looks v. late WW1 - early 1920's when the women's movement was at it's height so may be more of a political statement than anything else. What the significance of the cap badge is I can't say.
The badge resembles this more than the other.
It's the Ox & Bucks.
jim