Do I need a passport for my dog to travel from US to Europe.

This site link might help you.

Defra, UK - Animal health and welfare - Pet Travel Scheme (http://www.defra.gov.uk/animalh/quarantine/PETS/index.htm)

I had never heard of it before, but looked it up after I read your question. I had always heard there would be a quarantine period, but according to this link, it is possible that you can follow the procedures to avoid that process.