When I had a store selling in the UK (as a US based business) we used Amazon FBA to fulfill EU orders, and then listed our products on Amazon UK. Pretty nice setup, just a pain dealing with VAT haha.
Founder of Speed Boostr (Shopify optimization and dev agency). Creator of Theme Scientist (A/B testing app). Creator of Order Automator (app that auto tags + fulfills orders, send emails). Creator of Tip Jar (add a tip button to your store). Creator of Shopify Analyzer (free performance analysis tool). My team also builds custom apps and automated solutions. Enjoy the adventure!