The standard answer to this question is that QEII is the 40th monarch since the dynasty began in William the Conqueror. There were Anglo Saxon kings, and Danish kings before then but they are considered a different dynasty.
= The dynasty is not the same as a "house". The "house" changes several times.
- These 40 monarchs span 32 generations. Many times several brothers serve as monarch in turn. In one case a generation was skipped. Should QEII outlive her son Charles, that would be an example of skipping a generation.
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You will never get a completely unambiguos answer to this question. There have always been monarchs that had short reigns, like Jane (9 days) that aren't officially counted. Matilda is another who had a disputed reign which resulted in a civil war.
- The current dynasty is considered to have begun with William the Conqueror . but there are many kings who were considered king of England before him. Some include:
Edmund II , Ironside
Aethelred II , the Unready
Edgar
Edmund
Edward, the Elder
Alfred , the Great
Aethelwulf
Egbert (usually considered the first king of england).
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Plus their is the Scottish Kings (Scotland is part of Britain). To most people there have been two King James. King James I (of bible fame) and his grandson, King James II. According to the Scottish numbering system they are James VI and James VII respectfully. If Prince William were to name his son James, he would rule as King James VIII.