No idea, but courts generally do not like to interfere in the running of private organisations. Has any club successfully challenged an expulsion from the football league or any other football organisation? Hereford spring to mind from recent times.
How? The FL is pretty much a private members club and QPR could potentially break the rules of membership. I very much doubt that any court would want to intervene. Plenty of other clubs who don't break the rules waiting to take their place...