Would a mini allotment be a crazy idea?

This is the (very weedy) front of my Victorian terrace house. The back is not suitable for much growing. The front is south facing. I hate the slate and want to change it either way. Do you think it would be possible to grow some (food) things here? My current main concerns are ground quality and whether I can have an effect on that, and local cats/foxes pooing/weeing there.