Hi
If you do not wish to sign up with EE for an iPhone service plan that also includes support for the built-in cellular on Apple Watch Series 3 (GPS + Cellular), then you cannot currently use that feature.
However, when using a different carrier's service plan for your iPhone, 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.
Apple advises that additional carriers are being added all the time.
Users elsewhere have reported that Vodafone, for example, has advised via online chat support that it will announce service plan support for Apple Watch Series 3 (GPS + Cellular) later this month, with availability beginning in November:
iWatch 3 Cellular Support - Community home
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: