Not really; the rule is the same everywhere, but everywhere there are people who don't find it logical, so they do the opposite.
I've always put punctuation inside quotation marks, such as: "He said she was lovely."
Someone has told me that in England they go outside of quotation marks, such as: "He said she was lovely".
Do they do it that way in England?
Not really; the rule is the same everywhere, but everywhere there are people who don't find it logical, so they do the opposite.
This is a rather enjoyable explanation of it.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
I grew up reading British English, and never noticed such a convention. For instance, in George Allen & Unwin's series, the Hobbit & Lord of the Rings, the convention you claim is British was never used.
Could it be recent?
I've just had a flick through various London-published novels by Penguin, Pan, Harper, Viking. They all put the period inside.
However, the period doesn't come inside in the following type of case from Wild Swans Harper:
... with the disastrous consequences of the Great Leap, which I had known only as a "glorious success". (p.529)
Many women went into hiding for fear of their "liberators". (p. 78)
I tend to often put the period on the outside. I don't think it matters much - perhaps because it's the only piece of unorthodox punctuation I regularly use. And I possibly use it here because a lot of the examples are like those above, e.g.:
Only he would call something a "schoolyard retort".
I agree, it's reasonable to do so if deliberate.