That was one of the major things American service members were taught to expect when ordering pop/fizzy drinks in the UK - don’t expect ice (and don’t ask for it).
The problem was the refrigeration - just anecdotal, but I found ordering a Coke in the UK, regardless of the establishment, resulted in getting a room temp drink maybe 70% of the time. Sometimes, even the refrigerators at the food shops were less than ideal, barely chilling anything.
It could be cultural that way, too, though, because I do know that a lot of us like our drinks to be teeth-numbing cold. I’m drinking a seltzer-and-lemon right now, single serve can, and I’m using nine (that’s right, nine) large ice cubes…and that can was straight from the 44F fridge.