By the year 1135, there were no legitimate, direct male descendents of William the Conqueror. The crown of England was hotly disputed between his grandchildren Matilda and Stephen, in a civil war known as the Anarchy. When the war ended, Stephen held the throne - but only condition that Matilda's son Henry would be his heir.
When Henry II ascended the throne, he founded the line of the Plantagenet kings. Over the next few centuries, the succession law in England was often debated, and different interpretations used to support different kings. England did not adopt Salic law - the French system whereby no woman could ever hold a place in the line of succession - but... what if it had?
(Answer: nothing would have been different, and the House of Plantagenet would still have gone extinct in the male line by 1500.)
Historical monarchs are bolded. Other members of the line of succession are italicised. Only children and consorts relevant to the succession are included.