Learn English – Is it appropriate to call a British person a “Brit”

I would ask the question in this way: "How familiar are you with X?".

Asking "Are you familiar with X?" suggests that the answer is either yes or no, while my question is "accepting" to all levels of understanding.

The country of which I am a citizen is the United Kingdom of Great Britain and Northern Ireland. Great Britain is the largest of the British Isles and is home to England, Scotland and Wales. I was born in England and, apart from several extended periods abroad, have lived my life in England. That makes me ethnically English and politically British. Although Great Britain is a geographical term, British describes nationals of the whole of the United Kingdom and Britain is sometimes used to mean the United Kingdom. Things are often perceived differently abroad, and even by some of the British themselves. The whole political entity is frequently referred to as England, even though England is only a part of it. That doesn’t usually bother the English, but it might bother the Welsh, the Scots and the Northern Irish. The best policy is to call the country the United Kingdom or, less formally, Britain. Call the people British, unless you know them to be English, Welsh, Scottish or Northern Irish or something else.

EDIT:

The title ‘The United Kingdom of Great Britain and Northern Ireland’ raises an interesting linguistic, as well as political, point. Syntactically, it’s ambiguous. Is it ‘(The United Kingdom) of (Great Britain and Northern Ireland’) or is it ‘(The United Kingdom of Great Britain) and (Northern Ireland)’?

In ‘The Isles: A History’, Norman Davies traces the various titles by which the isles have been known. From 1660 to 1707 it was ‘The Kingdom of England and Wales’. The union with Scotland in 1707 gave us ‘The united Kingdom of Great Britain’. Meanwhile, there was a Kingdom of Ireland from 1660 to 1800. In 1801, Ireland was included in ‘The United Kingdom of Great Britain and Ireland’. That state of affairs lasted until 1922 when Ireland divided, allowing the six northern Irish counties to become part of ‘The United Kingdom of Great Britain and Northern Ireland’.

The original ‘united kingdom’ of 1707 was so called because it united England (with Wales) and Scotland. The addition of ‘Ireland’ in 1801 and of ‘Northern Ireland’ in 1922 can therefore be seen as mere accretions to an already united kingdom. However, the grammatical ambiguity allows the alternative interpretation of all components of the State being united under a single crown. A good example, perhaps, of Engli-, sorry, British, compromise.