When I looked at this last time, I
think I found that the style in several national British newspapers (at least) is to put the period inside if the quote that ends the sentence is a complete sentence in itself, otherwise outside. Your example seems like a complete sentence, so the period would go inside. On the other hand, in the following, the period would go outside:
The president called it a "disaster".
How far this reflects a consistent "British" style I'm not sure.