Apple Watch USA - UK?

A GPS+Cellular Apple watch bought in the U.S will not work with cellular carriers in the U.K. It will work as a GPS-only watch.

A GPS only watch will work anywhere in the world, but has no way to have cellular service when away from the paired iPhone.

Apple Watch - Carriers - Apple - https://www.apple.com/watch/cellular/

"To cover the LTE and UMTS bands used around the world, there are two separate models for Apple Watch Series 5, and three for Apple Watch Series 3.2 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 roaming 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.

Building on what Phil0124 said, a GPS only Apple Watch will do Everything a cellular model will do as long as your Mum's iPhone is nearby. The cellular model can leave the iPhone at home while you Mum goes for a walk, run, bike ride, etc...

What the Apple Watch GPS-only can do without an iPhone (there is information about the cellular model as well)

https://support.apple.com/en-us/HT205547

https://www.imore.com/heres-what-apple-watch-can-do-without-iphone

GPS vs Cellular

https://www.imore.com/apple-watch-cellular-vs-gps-whats-difference