Hi
Yes, it will - without any limitations, including in respect of GPS. There are no regional differences in hardware for Apple Watch Series 3 (GPS).
The Apple Watch can be used in any country in conjunction with an iPhone 5s or newer model of iPhone (running the latest version of iOS) and a service plan for the iPhone from any carrier:
Set up your Apple Watch - Apple Support
Apple's Limited Warranty terms for an Apple Watch purchased in the US are detailed here:
Apple One (1) Year Limited Warranty
If bought in the US, then the included USB Power Adapter will have pins localised to the US.
The Apple Watch can be charged in the UK by using a local version of the Apple USB Power Adapter for iPhone or iPad, using a travel adapter, by charging via USB or by purchasing a UK USB Power Adapter as a separate accessory:
Power & Cables - Watch Accessories - Apple (UK)