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.