Often times, when two kanji come together to form a kanji compound (or jukugo), you use the on'yomi readings. This is similar to that, though instead of another kanji it's a foreign word. This pattern works with almost any country as well. Just add 人 to a country name and you've described the people who live there. You'll see more of these before you're finished here.
And since 人 has two on'yomi readings, here's a mnemonic to help you remember which one to use:
As with all words for nationalities, the 人 here is pronounced じん. All nationalities, including Brits, love jeans (じん)!
That British person with the straight nose speaks in a nasal voice.
Apparently, this British person hasn't tried ume vinegar before.
I got a friend request from a Brit I don't know.