It's not saying you don't know. It's saying that, this should be part of your knowledge based on you being British.
I don't see how that's offensive.
"If you were British..." and "If you are British..." have very different subtext.
That specific form of the sentence has negative connotations and might be considered divisive in (British) English.
It's essentially a challenge to my honesty, and had you said "if you are" rather than "if you were" it'd be a more amiable challenge, implying I should respond with proof that I know where York is, and not suggest I'm being dishonest.
As I said, it's divisive, but to some may be considered offensive too.
Just one word makes all of the difference.
If you want to suggest I would know where York is by virtue of being British, you might say;
"You will know where York is, because you're British" or "You must know where York is, you're British".
The statement is at most doubting whether you are British, but not dismissing or claiming the opposite.
>but to some may be considered offensive too.
It's offensive that someone might claim to be from somewhere and not understand a very common piece of knowledge from that place. Or at least I might want to claim it to be.
It's completely normal to qualify one's perspective, and often beneficial. in fact for people to know whether your comment is an opinion, or based on some actual experience, knowledge, skill, etc, it adds value to the discussion.
In the context of South Korean culture, it's absolutely useful to know the commenter is South Korean.
If we're talking about tea, crumpets, or the rain, I might point out that I'm British.