The House of Plantagenet is the name given in England's historial narrative for the 14 Kings that ruled for the 331 years from 1154 to 1485.

We can see from the above trees that the current House of Windsor is decendanded from the following Houses.
York House
Tudor House
Stuart House
Hanover House
Windsor House

What I am mainly concerned with is the House of York. For this article, the Beginning is with Richard Pantagenet also known as Richard of York and his two sons Edward IV and Richard III. Before Richard III could be crowned, Edward IV's marriage to Elizabeth Woodville was publicly declared to be invalid, making their children illegitimate and ineligible for the throne. On 25 June an assembly of lords and commoners endorsed these claims.

Cecily Neville born May 3, 1415 married Richard Pantagenet (Richard of York) at the age of 14 in 1429. He was 18. In the summer of 1441, England was at war with France. Richard Pantagenet went to Pontoise to engauge the French. While Richard of York was away at battle, Cecily Neville was rumored to having an affair with an archer who was based in the Royal Garrison. Nine months later Edward IV was born on 28th April, 1442 in Rouen, Normandy. Cicily was 26 years old.

During Edward IV's lifetime and even after his death, persistant rumors about Edward IV's legitimacy abounded. Even Shakespear wrote a comment about Edward IV's illigitimacy in his play Richard III (Edward IV's brother).

"When that my Mother went with child, Noble York, my princely father that had wars in France and by true computation of the time, found that the issue was not his begot." Act III scene 5. Shakespear being very cleaver, could not outrightly say that Cecily was unfaithful to Richard Pantagenet so the word "issue" was used to mean "a particular problem at hand" and "begot" to mean "not of his making". So the line could be interpreted as, a particular problem that was not created by Richard, thus cleaverly disguising the real meaning of issue(Edward IV in her womb) was not of his (Richard Pantagenet) begot (love making).

Edward IV was born on 28th April, 1442 counting back 40 weeks, puts the time of conception in the Fall/Autumn at the week of Sept. 16-22, 1441 when Richard Pantagenet was in Pontoise and as such, the line of legal throneship from Edward IV to Queen Elizabeth II was completely illegitimate.