Sparkplugs traditionally have metric threads and inch size flats. You need a 13/16" socket (nominal size) = .8125" = 20.66 mm
Measuring a BR8EG spark plug shows .805" actual = 20.45 mm
A standard spark plug socket (Husky, Snap On etc.) has a shallow hex and clears the water outlet. There may be some variation between brands of sockets.
As stated the stock sheet metal wrench fits OK.