Except that a quotation that doesn't end the containing sentence isn't punctuated that way in either US or UK style; with the added text, it would be either:

(UK) Dr Johnson kicked a large rock and said, as his foot rebounded, ‘I refute it thus’, and then said no more.

or:

(US) Dr Johnson kicked a large rock and said, as his foot rebounded, “I refute it thus,” and then said no more.

But there you have just come to the same British conclusion that the end of the sentence is outside the quotation.