Queen Elizabeth I would be a distant cousin of Queen Elizabeth II. Both Elizabeths are descentants of Henry VII.
Elizabeth I was the granddaughter of Henry VII through her father Henry VIII....
Elizabeth II is called Elizabeth II not because she is a descendant of Elizabeth I, but because she is the second Queen in England with the name Elizabeth.
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Queen Elizabeth I reigned...
Elizabeth's Daughter.
Elizabeth never married and she never had children, thus the nickname the "Virgin Queen". When she died, she was succeeded by James VI of Scotland, who became James I of England.