What a saga. We began in July 2007, and our dog just arrived in the UK today. Lots of stress and worrying, but she is just fine (a little jet-lagged and confused, but generally happy). The people at the Animal Arrivals Centre at Heathrow were so nice to our girl, as well.
I originally was trying to tackle the process of our dog moving from Seattle to London via the PETS scheme by myself, without a pet mover. It would have been do-able, except for I got so stressed out about doing everything right that I ended up hiring someone that British Airways recommended. Our move was complicated because we needed to be over in London in October, and our dog wasn't ready until February. She stayed with a family member in Seattle, and so I was making arrangements for her from a long way away.
I would recommend hiring a pet mover if you can find one that does it at a decent cost from your city. Overall cost was $2500, including airfare, freight charges, a huge crate, and having a pro do a lot of the paperwork. I hired the pet mover when we were already in our 6-month countdown, so I already had a lot of the initial steps done.
If anyone has any questions about Seattle to London specifically, feel free to ask! I am just so happy we have our dog again and that everything is over with!