OP seems absolutely miserable in her present job. OP since you have an idea relating to policy/project work, do you have project experience and can you at least try to acquire project experience/shadow in your present organisation (I don't want force you but even a months exposure could help). If not, third sector, local authority (go public) and even guardian offer loads of policy roles (however since you don't have experience you might have to start at a lower salary scale). Also policy involves loads of research are you OK with that, ensure that you do your research on this.
BTW when people are providing advice/suggestion you need to appreciative because often times your response is very dismissive (we're only trying to help you), when you're the one that it's benefiting from the suggested solutions. You have to be open because we don't know your full story and from our side it's like everything we suggest you say No or I can't to. I know you hate your current job and I completely understand now, but at least try ask for support on policy/project shadow in a different department at least, don't give up just yet.