I wouldn't say that the reason people in the UK haven't got air conditioning is because it's "bloody cold". Rather, it's because it's simply never bloody hot. I would even argue that the UK in general is
less cold than most of the US, for example the North East and Midwest.
However, I would go even further. The reason why no-one in Europe (for a loose definition of "no-one") has air conditioning is not so much the climate, but more heavily influenced by historical, cultural, and architectural reasons.
I'll bet that most current American homes were built after air conditioning was invented, their usual construction materials mean they are rarely well insulated, and single family homes are generally fully exposed to the Sun.
Compare that for instance with Spain, which one may assume would be hot enough to need air conditioning, with a climate comparable to that of California.
Some homes do have it of course, but it is never assumed by default. Firstly, most of the population lives in flats, which mean their homes are less exposed to the Sun (except attics), and construction materials are generally sturdier and better insulators by default. Secondly, old homes in villages have been there long before air conditioning was a glint in the ice cream man's eye, and thus have been designed over time to be better protected from the heat. Modern houses, even if they may be designed to accomodate potential air conditioning, are still more or less influenced by these ideas to an extent.
On the cultural aspect, as air conditioning has never been a given, people have learnt to adapt their lifestyles and expectations to living with the heat, and don't instinctively feel the need to have air conditioning blasting all the time. Of course people do like it and appreciate it when available, but it simply doesn't have the cultural expectation that it has in the US.