thanks to the evidence from Cecily Neville (the mother of both Edward IV and Richard III) that she'd had a fling with a groom and Edward IV was not a Plantagenet.
I must here protest that it is by no means proved that Cecily Neville ( a very pious lady) gave evidence that she had a fling with a groom. Some people believe this, but it is by no means accepted by all historians. If Edward was her son by her husband then the marriage of her granddaughter, Elizabeth of York, to Henry Tudor insured that the present Queen is the descendent of the Plantagenets. http://www.richardiii.net/r3_mother.htm
There is no way to prove it now at any rate.
Well the gestation period for Edward IV would have to have been suspiciously long - something like 15 months, if he was a Plantagenet, as his father was mostly away at war during that period. I think Channel 4 did a programme about it with various historians showing proof of the dates.
I understand that the Titulus Regius that Parliament passed making Richard III king was mainly based on Edward IV's marriage to Elizabeth Woodville being bigamist.
Apparently Edward IV liked to get about, but some high born ladies refused to sleep with him - so he married them secretly, making them and the priest promise not to say anything. The priest promised because Edward was King and the silly women promised because they hoped to be Queen. The marriage to Elizabeth Woodville was also one of these secret marriages with no-one from the King's family present - but I think Edward IV loved her because he then introduced her to them and made her his official Queen. Unfortunately the other lady was still alive when Edward IV married Elizabeth, making all their children illegitimate.
Therefore Elizabeth of York was illegitimate and unions between her and Henry could pass no Plantagenet line down because Henry too only had a weak illegitimate claim via the Beauforts.
P.S. An 18th century Member of Parliament, Horace Walpole wrote a famous book about Richard III
It's luckily out of copyright and free for anyone to read. here it is: Historic Doubts on the Life of Richard III
And here's a neat little paragraph from it:
The doubts on the validity of Edward's marriage were better grounds for Richard's proceedings than aspersion of his mother's honour. On that invalidity he claimed the crown, and obtained it; and with such universal concurrence, that the nation undoubtedly was on his side --but as he could not deprive his nephews, on that foundation, without bastardizing their sisters too, no wonder, the historians, who wrote under the Lancastrian domination, have used all their art and industry to misrepresent the fact. If the marriage of Edward the Fourth with the widow Grey was bigamy, and consequently null, what became of the title of Elizabeth of York, wife of Henry the Seventh? What became of it? Why a bastard branch of Lancaster, matched with a bastard of York, were obtruded on the nation as the right heirs of the crown! and, as far as two negatives can make an affirmative, they were so.
They didn't mince words back then! (Widow Grey was Elizabeth Woodville - she had already been married and widowed by the time she married Edward IV).