Overall, I think the UK is moving toward the drink temperatures preferred by us in the US. Most pubs I visit proudly display their "Super Cold" taps of mostly American beers claiming they are as close to freezing as possible (which although another topic, is pretty much the only temperature you should drink US beers to hide their lack of taste). I have no problems getting a Coke or other soft drink in a fast food place with more than enough ice. Even bottled water is sold icy cold in snack shops and grocers. If I remember right, I even saw bagged ice for sale at one of the shops around St. Pancras station my last visit (right before the heat waves started this summer). There are a few restaurants which give only 2 or 3 pieces of ice in drinks still. They are always happy to provide more if asked.
The other thing is that in the US, most drinks in restaurants (non alcohol only and excluding milk and fruit juices) are served with unlimited refills where in Europe and the UK you pay individually for each glass you get. So if you can drink all you want for one charge, does it really matter if the glass is mostly ice? If I was paying $3.00 a glass for drinks in the US without refills and I got a glass of mostly ice, I would not be happy. Same in the UK.
Interesting thing about ice in drinks. Starbucks in the US got sued because their iced teas had "too much ice" according to one customer. Drinks served in the winter with ice appeared to have more ice than those severed in the summer. So now Starbucks (at least the ones near me) puts about half the ice in their teas when the temperature is below 45 Fahrenheit. Works OK except when you get a freshly brewed batch of tea that has not cooled off yet so all the ice in the glass melts leaving you with a luke warm drink.