My MCs are looking for an old tomb. The latest lead to it's location is a journal entry from the 1750s, saying it's in British territory. It's gonna turn out to be in New York, which was at the time, owned by the British. Do you think readers would think about what territories Britain owned at the time, or would they think, "Oh, it's in Britain." and only imagine modern day Britain (the story takes place modern day)? I am hoping for it to be a surprise. Would you make the connection? And don't worry about the whole "why did the British build a tomb in their colonies?" thing, they weren't the ones who put it there. Long story.
If I saw the phrase "British territory" I would think of all of the international holdings of the British.
I think even if your readers did think "Oh it's in Britain", it would make for a nice potential "twist" The ones who didn't see it coming would be like "Well DUH!" when they do find out I also like it that it sorta turns the tables a bit - these days most people think of America as the ruling giant. To play on the fact that Britain once ruled what is today America in a modern novel - maybe it's 'cause I'm British, but I kinda like it Also, when your MCs find the clue, they'll likely discuss it. You could always have a character say, "Britain? Surely not!" and another smarter character say, "Well, Britain had quite the empire..." List a few of its colonies, and then say, "Any of these would have been part of British territory. We've got a long way to go yet, folks!" You get the idea.