What was there before the Royal Society? There were still universities, wasn't that 'Academia'? Or is there a specific meaning to the word 'academia' I don't know?
I'm not claiming the Royal Society 'invented' peer-reviewed science. It wasn't a dramatic moment of epiphany, just a gradually growing insight that spread through society. And the Royal Society was at its forefront.
To get an idea of the formation of empirical science in Europe read Quicksilver by Neil Stephenson ~ https://en.wikipedia.org/wiki/Quicksilver_%28novel%29 & a quick synopsis here ~ http://www.wired.com/wired/archive/11.09/history.html