No information on this vessel was given beyond its appearance in the opening credits of Star Trek: Enterprise. That she was British is assumed by her bearing the prefix "HMS". That she was a galleon is evidenced by her depiction.
Historically, the Royal Navy has had two ships named HMS Enterprize (spelled with a 'z'): an eight-gun sloop captured from the Spanish in 1743, and a ten-gun tender later captured by the Americans in 1775. Neither were galleons.