We've had a lot of success with keeping cats out (our next door neighbour has 2). On top of the bit of fence and gate we have, we've put prikka strippa (stops them jumping up - they only try once) but by law you HAVE to put a notice on either side to stop humans getting injured (we were glad to have done this to stop our window cleaner climbing over). The bit with a hedge - my husband erected a chicken wire fence at the bottom to close up all the gaps. Then we got a Catwatch (electronic gadget that gives out a signal when anything walks past - dogs, birds, humans, don't hear it but cats do. So far, fingers crossed, it all seems to be working. barriers is definitely the way to go, if you can, so first identify their favourite route in.