According to various books on Historical buttons, "rolled-brass" 1-piece buttons began to be backmarked about 1790 (perhaps a few years sooner). The earliest backmarks on them were written in raised lettering, like you see on the button at the top of this discussion-thread. Indented lettering on them began to be used about 1810. These plain 1-piece buttons fell out of favor with the public in the late-1830s, due to the advent of machines which could INEXPENSIVELY produce very-ornate 2-piece buttons. So, your rolled-brass 1-piece plain-front flatbutton with an indented-lettering backmark was made in Britain sometime between 1810 and (at latest) the early-1840s.
In case you don't already know... they were manufactured in the multi-millions for use on civilian clothing, not military. However, we know that a (very) few did get used by "poor" Militia soldiers.