Briton is the correct demonym for a citizen of the United Kingdom[0]. Britons is the preferred way to speak about all residents of the British Isles without having to use a qualifier, e.g. British people, People of Britain.
Compare Finland, Denmark, Scotland.
[0] http://en.m.wikipedia.org/wiki/List_of_adjectival_and_demony... [1] I'm a British Citizen