Is it possible to do a PhD in Environmental Policy and Economics if I do not have an academic background in Economics?
Sure you can. However make sure your supervisor(s) know the economics better (e.g., by looking at his/her current publications) than you. This is because if the supervisor doesn't know the area very well, he/she doesn't know if your work is in fact a contribution because he is not an experienced yet; and therefore it will create a very unpleasant situation in which you work hard; without knowing you are on the right track.