That's a problem with a small coop, not enough room to handle much. But lots of people deal with it. The only way I've broken a broody is with a wire bottomed cage, though I really haven't tried any other method.
What you need is a predator-secure area where you can put an elevated cage, either hanging or blocked up. Something like those wire dog cages work well. How secure is your run? Do you have another outbuilding or possibly garage where you could put a crate? I'd think in Suffolk she could handle being outside this time of year, but you might want a cover to protect her from rain. Three full days and nights in the cage usually works.
Not much help I'm aware but I don't know what options other than the coop itself you have. Good luck!