Can I use Apple Watch Series 8 bought in the US in UK

Differences in Watch functionality between countries depends largely upon if it is a cellular or GPS-only model, and then to the degree your iPhone and Watch work with the cellular services in the places where you are using your hardware. This is discussed in this topic --> https://discussions.apple.com/thread/252732160

Check the list of Apple Watch carriers provided in this page --> Apple Watch - Carriers - Apple

"To cover the LTE and UMTS bands used around the world, there are two separate cellular models for Apple Watch Series 8, Apple Watch SE, and Apple Watch Ultra. They have been optimized for use in the country of purchase, and not all models work in all countries or regions. There is no single model that supports cellular service worldwide. To see which carriers in your country or region offer cellular service for Apple Watch, refer to the chart below."

Click on the link to read more.