After reflection (and another coffee) I think you're right - the "great mon" is the supreme arbiter, & if an appeal to him didn't sort things out she'd be willing to fight.

It's quite a complex thought, actually (this may be the second coffee talking) - if she had clothes (or clogs) to put on, she'd go to London, and if that appeal didn't work then she'd fight. But the song's just established that they're dirt poor, and for just that reason they're never going to get the chance to appeal to the King - and by implication they're never going to fight. It's like a rather dark version of "There's a hole in my bucket" - "I'm too poor to afford decent clothes, I'd fight for my rights but I should appeal to the King first, but I can't appeal to the King because I haven't got any decent clothes".