Or perhaps it's just on their 4G?

EE is branding confusion hell. They're a result of the merger between Orange and T-Mobile, but depending on situation you'll either have them treat you as an "EE customer" or as a T-Mobile/Orange customer. The only ones who are "only" EE customers in their eyes appear to be 4G users.

My contract was entered into with T-Mobile, and is a personal account, and I have never seen a block, including testing just now with obvious candidates.