The death of Elizabeth I without issue saw the crown go to James I/ VI of Scotland, the son of Mary Queen of Scots, as her heir, which united the Scottish and English thrones and brought in the Stuart dynasty.
The Stuarts were the monarchy in charge during the lead up to the English Civil War and the execution of King Charles I saw a brief end of the British monarchy. Oliver Cromwell and his son, Richard, were named as Lord Protector and ruled until the monarchy was restored under Charles II. His son, James II, was openly Catholic, which caused some tension with parliament and saw his daughter, Mary II being instated as monarch instead.
Queen Anne, who reigned for 12 years saw the British monarchy up until the Acts of the Union, which officially joined the Kingdoms of England and Scotland into the Kingdom of Great Britain.
Here are the Stuart monarchs, and Oliver Cromwell.