Its simply a matter of beer styles. In the US, Pilsner-style lagers predominate and these are supposed to be consumed very cold (and fizzy).

On the other hand, in the UK, ales have predominated until quite recently. These are not fizzy and are best consumed at cellar temperature.

You would no more drink warm lager in the UK than anywhere else - think of lager and ale as being analogous to sparkling white wine on one hand and red wine one the other.

You would no more drink warm flat champagne than a cold fizzy primitivo.

TL;DR The type of beer that became popular in North America is fermented and stored at a lower temperature than those preferred in Britain.

I'm not exactly a historian, but I am a trained and licenced cellarman in Scotland (and have also worked in the US). I think that this question can be answered in part by challenging the underlying assumption that beer actually is colder in N.America than it is in Britain. It depends on the type of beer. I'll try to keep my answer as succinct as possible. Traditional British beers (such as bitter, stout, and real ales) are called top-fermented. They ferment at warmer temperatures and as such aren't stored as cold as bottom-fermented beers (which I'll get into in a second). Part of the reason for this is that being in the cellar is part of the maturation process for these beers. Bottom-fermented beers ferment at lower temperatures. The lager-style beers that became popular in America (though Bavarian in origin) use this kind of fermentation process. The yeast used in the fermentation process sinks to the bottom and a clearer beer results. Anyway, when each of these styles of beer moved away from their original homes, they took the storage and serving temperature with them.

This is purely personal experience, but as an English person (and ex-bar manager) with American family, I don't know what you are referring to, lager is a lower temperature than ale generally but it is not "British" to have warm(er) beer.

Lagers, such as what you are probably referring to as "American" are served at a low temperature more or less world wide. They are generally chilled in their pressurised pumps.

Ales, Stouts and other top-fermented beers are served at "cellar temperature" which is around 11 Celsius. There are many resources to examine why this is the case. But typically in England they are operated by a non-powered hand pump that does not chill the ale.

Of course there are many, many variations and exceptions (wheat beer is a top-fermented ale that is served at a much lower temp than most ales for example), but based on my experience there is zero difference between lager temperature in the UK versus America, although it should be noted that it is extremely rare to find genuine, hand-pumped ale in non-pressurised hand-pumps in the US (in my experience).