They ended the monarchy when they beheaded Charles I. Then after Oliver Cromwell died, the country fell to pieces, and begged his son Charles to come back and take the crown. England's problem is that since the Act of Settlement in 1701, they will only allow a Protestant to hold the throne. When Charles II died in 1685, he had no legitimate heirs, and his brother James II inherited the throne that year, then converted to Catholicism. He was driven from the throne in December 1688, and fled to France for the remainder of his life. His daughter Mary, who was married to William of Orange. Both were Protestants and took over the throne. Their daughter Anne inherited the throne in March 1702. She had no children that lived, and the crown passed to George I of Germany. During the First World War, the English Royal Family chose to change their last name from the German Saxe-Coburg and Gotha, to Windsor because of anti-German sentiment in the U.K.
Without the monarchy the UK would split into at least 3 countries. That would not be good for residents of the British Isles, Europe, the USA & the world!