Now you mention it, I can't remember whether many European languages even do have a well established term for "British" as opposed to "English". I remember learning words like "anglais", "Inglese", "Englisch" etc. in language lessons at school, and the impression I got at the time was that those were the generally accepted terms for UKians in those languages. (Though I don't remember stopping to get the point clear at the time.) Have they all become up to date now, so that there are better terms in widespread use?

The terms certainly exist, in French (British, Scottish, Welsh, Irish):

Les Britaniques, les Écossais, les Gallois, les Irlandais

(We should not confuse the Welsh with cigarretes)

In Spanish:

Los Británicos, los Escoceses, los Galeses, los Irlandeses (through you could probably get away with "los Norirlandeses" for the British lot)

The Spanish have an obsession with Demonyms ("Gentilícios"), and every little town and village in spain has its own demonym, some les obvious than others, as well as major international locations, such as London (Londinense) and Edinburgh (Edimburgués), and even manage to differentiate between someone from the USA (Estadounidense) and the continent of America (Americanos).

That being said, the use of such demonyms for the Scottish and Welsh is not common in day-to-day use, and people prefer to just refer to the entire population of the United Kingdom as "The English" rather than the more correct "British".

And whilst the Welsh don't have much to crow about, most languages have a word for Scottish, as that's where the whisky comes from.