Your guess is correct... it is an 1820s brass 1-piece construction New York State Militia button, made in Britain. The fancy lettering in the backmark is called Old English Script. By the way... in button backmarks, the word "plated" always meant silver plating. Gold plating was called gilt.
Thank you for the replies and it is really nice find. Would like to know if it is rare because it was made in England as opposed to here in the states?