All British Monarchs are descendants of Elizabeth of York.

Who in turn can trace her descent through her father Edward IV, to (at least nominally if you believe her great grandfather Richard of conisburgh was legitimate) to Edward III, and hence to the first Plantagenet king Henry II.

Henry II was the son of empress Matilda, who in turn was the granddaughter of William the Conqueror.

The Queen can trace her ancestry back to Alfred the Great, King of the Anglo-Saxons (871-899). Alfred was descended from Cerdic, first King of Wessex (519-534) who invaded Britain from a Germanic land. According to the mythological genealogies in the Anglo-Saxon Chronicle, Cerdic was a descendent of the god Woden.

Queen Elizabeth II can trace her descent as far back as King Egbert, who ruled England in the early 800s AD. Here is a family tree showing the line of ancestry from Queen Elizabeth II back to King Alfred the Great, and here is the family tree connecting Alfred to to King Egbert.

You'll notice that Queen Elizabeth II's line of ancestry does not run through some previous monarchs of England/Britain: for example, she is not descended from Queen Elizabeth I, who left no children. Nor is she descended from any of the later Tudor monarchs: Edward VI, Mary I, Henry VIII. That branch died out, and the inheritance jumped across to a collateral line of descent from the first Stuart king of England, James I, through the German House of Hanover, to King George I of Britain. The last Tudor monarch that Queen Elizabeth II is descended from is King Henry VII - via his daughter's marriage to a Scottish Stewart king.

She's also unlikely to be descended from the later Stuart monarchs of Britain (although, she might have some descent through a non-royal line somewhere).

So, Queen Elizabeth II is not descended from at least some previous British and English monarchs. However, all British and English monarchs can trace their origins back to King Egbert.