Thanks again, everyone, for the replies and advice. Sorry I haven't replied to all of the comments individually - we have limited internet access at the moment and have just had a 2-day outage!
Ziggy is doing so well, and seems to be much more relaxed most of the time. I think he's starting to trust us, and to trust that we don't mean him any harm. When he does get anxious, it's usually when he's confronted with something a bit different - he loves his routine drive/afternoon walk with me, but when my husband tried to take him yesterday he was a bit confused and there was some very gentle growling. He also seemed confused when we took him in the car to drop my daughter at the station, as this was in the early morning and there were 2 of us, but eventually settled and seemed to enjoy the outing.
He has been really affectionate this morning, seeking us out, jumping onto our laps, following us around, rather going off somewhere by himself after a while. So it seems that there's a really sweet affectionate little pup under all that anxiety. I feel so relieved for him because he seemed so stressed an constantly on guard when he first arrived. Of course, he still has his panics (when there's a sudden noise or when he starts slipping of my lap) but he seems so much calmer.
After more than a week of NO interaction with our cat, he also seems more relaxed about her - if we walk past the room where she is sitting and he can see her, he pulls on the lead a bit and would like to get closer to her, but he's quite calm about it and doesn't bark or growl. So I think as everyone suggests we'll just take it REALLY slowly and see what happens. The cat is gradually relaxing, too, and as she always spent most of her time in the bedroom I think they'll eventually come to some sort of understanding, as you suggest JudyN.
I must admit that when I posted my first question I was feeling quite overwhelmed by Ziggy's anxiety, and especially the growling/snapping, so I'm really grateful for all your suggestions that have helped us to get to this stage.
