Waymo is basically unique in offering Level 4 Self Driving (hence this article) and they only do this in a small number of locations in the US, such as (parts of) Phoenix - so, yes, you're correct that in the UK, or indeed anywhere outside of those few locations, there aren't real "Self Driving" cars.
You won't know if people have Level 3 "Self Driving" cars because unlike Level 4, the Level 3 cars always have a human sat in the driving seat, it's just that maybe the human isn't paying attention and maybe the car is driving anyway. It may be difficult to gauge (beyond guessing) how many people you see are bad drivers and how many aren't actually driving at all under L3...
L1 (the machine does some of the work but a human driver is always doing much of the driving) is certainly something you see and don't even think about. Intelligent Cruise control (ie it won't smack into the car ahead but instead slow down) on a motorway, maybe automatic lane keeping on somebody's fancier or newer car, it's not "Self driving" as you'd understand it, but it's something.
The way these "Levels" work is L3 to L4 is the point where we transition from "The human is legally driving but the machine is offering more and more assistance" to "The machine is legally driving and the human is asked less and less often to do anything at all". As a result a person who is literally blind and thus couldn't possible drive the car or obtain a license to do so - can (and they do) use a Waymo, just like they'd use an Uber, but they cannot do the same with Tesla "Full Self Driving".