There is no single set of "British rules" for when you put a full stop inside and when you put it outside the quotation marks. Different British publishers have different rules.
Look at this article from the Guardian, which gives examples of the different rules that different publishers have. One thing the author says is that putting a full stop outside the quotes in the situation you are asking about, when a full sentence is quoted, "makes me shudder." So to keep the Guardian from shuddering, I would advise putting the full stop inside in this case. The Oxford Guide to Style also recommends putting the period inside the quote if you are quoting a complete sentence (except if the quote is a "explanation or specimen", and while they give examples of these, I think this is to some extent a subjective decision).
[But, for example, should the full stop after "makes me shudder" in my sentence above go inside or outside the quote? Some publishers would say outside, because a full sentence isn't being quoted. But I believe others would say inside, because there was a period there in the original quote. I think either decision is fine, as long as you're consistent.]