Your mention of Tesco tells me you are in UK, and the only UK cellular support for the Apple Watch is as you say, EE. To use the standalone cellular features the watch has to be added as a secondary device on your iPhone‘s network account, so you can’t do standalone cellular via your Tesco account.
Having said that, the non-cellular functions will work through your paired iPhone on any carrier, and this applies for both the GPS only and GPS+LTE versions. The only thing you would lose is the ability to leave your phone at home and make calls etc from your watch. If you are content to carry your phone with you just get the GPS version - unless you are thinking to jump ship to EE when the LTE version would become fully functional.