Apple Watch on different network

I would think it unlikely but you'd have to ask O2 to be certain. FWIW I found EE offered the best support when I first got a cellular watch. I don't think O2 were doing it at the time, and Vodafone weren't doing visual voicemail so I ended up switching providers twice in a week. AFAIK you need to have both devices on the same network to have handoff between the devices work properly. Perhaps EE can match O2's offer.

tt2

Your iPhone and Apple Watch must use the same network provider, and you must be within your provider’s network when you set up cellular on your watch.