A small but necessary correction, just regarding the date. If a brass 1-piece flatbutton's backmark contains indented lettering, it dates from approximately 1810 into the 1840s. That being said, after the infant American button-making industry finally became capable of mass-producing brass buttons, around 1830, there was no longer much need to import buttons from Britain (which were more expensive, due to the US Government's protective Import Tariff on imported manufactured goods). So, your British-made brass flatbutton with an indented-lettering backmark most likely was manufactured sometime between 1810 and 1830.