Roundhead was the name given to the supporters of the Parliament (or Parliamentarians) during the English Civil War. They opposed King Charles I and the tradition of absolute monarchical power and the divine right of kings. The Roundheads sought greater powers for Parliament, and a constitutional monarchy. England's many Puritans and Presbyterians generally supported the roundheads. Some of the Puritans wore their hair closely cropped (in contrast to the long ringlets worn by men of courtly fashion), and the term appears to have derived from this distinction.
'Hanover rats' refers to the House of Hanover, and King George I of Great Britain (1660-1727), who ruled from 1714 to 1727. George was born in Hanover, in what is now Germany, and inherited the titles and lands of the Duchy of Brunswick-Lüneburg from his father and uncles. In 1708 he became prince-elector of Hanover.
After the death of Queen Anne of Great Britain, he ascended the British throne, as the first monarch of the House of Hanover. Over fifty Roman Catholics bore closer blood relationships to Anne, but the Act of Settlement 1701 prevented Catholics from inheriting the British throne. George, as Anne's closest living Protestant relative, got the crown. The Jacobites tried, without success, to depose George and replace him with Anne's Catholic half-brother, James Stuart.