Thomas,
Far be it for me to contradict your contradiction
, but the UK is a full EU member and has been since 1973! The common monetary policy and the Euro is only a relatively recent development and has little to do with EU membership.
Back to the quarantine and travel issue, the 'Pet Passport' scheme has been very well received here and in Europe. Basically, if your dog has been shown to be vaccinated and clear of rabies for a period of time, it can have a 'Pet Passport' which allows it to come and go from the UK. This means that dog owners in the UK can now take their dogs on holiday and take their bitches to studs in Europe. It also allows Europeans to bring their dogs over for shows and training seminars.
We're getting there, but we don't change too quickly!!