Thanks for using the forums to get this question answered, I can certainly appreciate your confusion as we've gone through a few changes over recent years.
We used to be on EE's network, some really old SIM's may still be on that one but we migrated most people over to Vodafone's network a couple of years ago. Now we are doing another migration over to O2's Network, some accounts may need a new SIM card to get this migrated over but it's usually a smooth process.
If you're a current mobile customer, do you need to know which network your SIM is on at the moment?
I'll be happy to help further if so 🙂