I agree with the mutterers when Rosie asked "British" and you said "No". Ireland was part of Britain in 1916, and remained so until 1920, IIRC. There are some that say Ireland is still part of Britain, but not "Great Britain", but I think that's a bit over(t)ly confrontational.

[Phil] Well, it all comes down to the meaning of Britain.

My preferred usage has always been to treat Britain and Great Britain as synonymous, referring (as a geographical term) to the island which makes up the bulk of England, Scotland and Wales, and more generally (and as a political term) to England + Scotland + Wales. Another view is that Britain (but not, I think, Great Britain) is synonymous with the UK; this seems to be your preferred usage. Wikipedia points me both to the Guardian style guide, which claims that "Britain is the official short form of United Kingdom of Great Britain and Northern Ireland", and also points to a quote from a British government website that says "the term 'Britain' is used informally to mean the United Kingdom of Great Britain and Northern Ireland" [my emphasis in both quotes].

So, having gone most of my life thinking I understood these demarcations perfectly, I'm now not sure. If anyone can point me to an official site which disambiguates "Britain" and "Great Britain" conclusively, I'd be grateful.

There is another subtlety (and here I am convinced, or almost), which is that "British" perhaps has a wider meaning than simply "pertaining to Britain". It is true, for example, that my passport of the United Kingdom of Great Britain and Northern Ireland describes me as a British citizen. On the basis of that distinction, I would accept that perhaps I should have said "yes" to "British?" though I might still disagree with your claim that "Ireland was a part of Britain in 1916". In any case, I thought my answer together with the audience muttering was a sufficiently non-misleading response.

To follow up, here are two sites that both seem reasonably reliable and that, taken together, support the view that (i) "British" has a meaning that extends beyond Britain in the specific case of nationality, but that (ii) using "Britain" to refer to the UK is at best informal and at worst incorrect. Here, we read:

BRITAIN. The informal name for the United Kingdom.
BRITISH is the formal designation of the nationality of citizens of the United Kingdom, and of certain others.

Compare with the following from here.

The adjective "British" is, of course, used in relation to Great Britain but there is also a common tendency to use it when referring to issues relating to both Great Britain and the United Kingdom. This is inaccurate and from a legal point of view erroneous. [emphasis mine]

Sometimes, however, in legislation the term "British" is used to refer to the United Kingdom as a whole, especially in matters relating to the question of nationality.

I'm not sure I am much wiser.

[CdM] I must re-examine myself. I have never in the past confused the UK with GB. I can't understand why I posted that. Although the time-stamp might explain it :-)