I doubt I can be of much help, but will try. We shipped from the US, not the UK, and used WorldCare Pet and were very happy with the whole experience. Also, we live in Gubei/Changning area so are further out from Pudong, but have not had any problems. We did have our dogs licensed, which we found to be fairly easy as long as we had everything we could possible need, and then some, with us when we went. When you are ready to do that, send me a message and I'll be glad to give you the steps we undertook.
The one thing I would recommend when renting is to make sure there is as much green space near you as possible. The locals in our neighborhood are very skiddish of dogs, even our smaller ones, and rather than walking them on the sidewalks and having to keep them right at our ankles, it's much easier to let them do their business in the larger grassy areas. But...be careful of left-behind messes from others when you walk through those areas....can't tell you how many times we've cleaned poop from our shoes because people can't seem to pick up after their pet.
There is a real estate company that I have seen on this site (
www.shanghaiprops.com) and they seem to cover all areas of Shanghai. You might contact them about possible areas in Pudong that are more "dog friendly" than others.
Hope this might help.