We cannot be sure.
The first reason is Britannia's size. While Britannia and its surrounding areas might be based on the real-world United Kingdom, the story considers it as a continent, not a country. This would mean that there is a possibility of Britannia being bigger than its real-world counterpart.
Another reason is that as far as I know, only Britannia was the focus of the story. There is no way to know how the other continents or countries are supposed to be like unless the mangaka reveals them.
Hence, we cannot check if Nanatsu no Taizai occurs in an alternate version of Earth, one with the same continents but different history and species.
Disclaimer: I have not yet read this series and this is based solely on research on the Internet so if there are any inaccuracies, feel free to mention them.