In busy areas the ESN will have additional sites exclusively for its use. Some of these are already under test e.g. in London.
Oh... I'd be very interested to see evidence of that happening in urban areas, very interested. EE are testing new 5G equipment in Canary Wharf and a couple of other locations, but I'd be pretty surprised if there were ESN-only sites in London. If anything, it seems to be the opposite.. that wherever EE can justify the cost of a new site, they want to get maximum payback which means full commercial service alongside ESN. In some very remote areas where even "we're the only network to have service" theories don't stretch, then yes you're right - "Extended Area Service" kicks in, where in some cases EE just install kit on a "government-installed" site.
Happy to take this to PM, but I'm not sure a VM forum is the best place for this :-(