(Across the border from England) In Wales, before the English conquest, blinding and castration was see frequently to render one's enemy impotent - if he wasn't able to (potentially) procreate and have an heir that would ensure smooth transition, he would not be able to lead men. There are many mentions of Welsh noblemen being blinded and castrated in the contemporary chronicles Brut y Tywysogion (e.g. 1127). You might find this article on family, descent and inheritance in the principality interesting - the author also mentions that Gerald of Wales, a chronicler of medieval Wales, acknowledged that the practice of blinding and castrating an enemy was common in the rest of Europe also.

These exemples do not refer, as in your question, to accidents at a young age, but they demonstrate the importance of certain attributes in society, in particular the ability to procreate. Whilst I don't think there is one single answer to your question, I think it is likely there were many occasions when a 'lesser' son would be passed over in favour of a younger one.

I am sure someone better versed in medieval English history might know of some examples.

Source: I did an undergrad and a postgraduate degree in Welsh History.

Not a physical deformity, but the example that immediately comes to mind is Richard III and his nephew, Edward the Earl of Warwick.

Edward of Warwick was his older brother George of Clarence's (who himself was executed) son. After the death of Richard III's own legitimate son he was the obvious heir to the House of York and the throne. But there is good evidence to indicate that Warwick was mentally handicapped and Richard disqualified him for succession, instead choosing his sister's son: John de la Pole, the earl of Lincoln. This is despite the fact that de la Pole's claim to the throne is inferior to that of Warwick's.

Well if you go strictly by law, which for England would have been male-preference cognatic primogeniture (eldest son inherits, females if there is no male) then there would be no distinction on whether or not the heir was in any way crippled. The crown (and/or other titles) will go to the eldest no matter their circumstance, if that person died with no children, then it goes to the next born son and ect. Now whether or not their liege should uphold that law is another matter entirely. The ruler would either need to circumvent the law or, like King William l, work out a deal with the eldest and hope that he deals with it. Essentially there are ways, and there are ways. If a ruler doesn't want their heir to inherit they can find a way, however, the law of the land was that the titles of the father was the birthright of the eldest. I'm not sure how likely it would be for a maimed son to lose his birthright, seeing as I don't know/can't find many instances of this and therein may be your answer.

Edit: Clarity