[jckt]

http://grammarist.com/usage/briton/

This link supports the opposite of davidgay's comment (sources within).

[alextgordon]

I can't say I've ever heard someone say "Briton" without the adjective "ancient".

[benjiweber]

It is a very common way of identifying someone as British. e.g. headlines such as "8 hostages, including 2 Britons", "X million Britons now live in <popular location>" are common.