You're welcome!
Apple Watch Series 3 (GPS + Cellular) models
EE is currently the only UK network that offers a service plan for your iPhone that supports the built-in cellular features on Apple Watch Series 3 (GPS + Cellular):
Apple Watch - Carriers - Apple
If you do not wish to sign up with EE, then you cannot currently use the built-in cellular feature on Apple Watch Series 3 (GPS + Cellular) models with another UK network.
However, if your iPhone service plan is with another network, then Apple Watch Series 3 (GPS + Cellular) can still be paired, set up and used for other features whilst skipping the steps to activate cellular. The cellular feature can then be enabled later, if and when you are using a compatible service plan on your iPhone, whether from EE or another UK carrier in due course.
You may wish to contact your preferred carrier to ask about their plans for providing service plans for iPhone that support Apple Watch Series 3 (GPS + Cellular).
You may also wish to monitor this page for further carriers being added over time:
Apple Watch - Carriers - Apple
Series 3 GPS-only models (and all other Apple Watch models)
Apple Watch Series 3 (GPS) and all other Apple Watch models 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.
More information:
Apple Watch - Compare - Apple
How to use your Apple Watch without your iPhone nearby - Apple Support