I think Westminster has the ultimate say in deciding who can be put on the throne. If the Prince of Wales slips up (like converting to Islam), or if he dies in some sort of freak accident (hint: many people claim that the MI5 will be so expert on covert operations that no one will ever know what they actually did), or the Queen sets up a parliament-approved will that the throne passes to William instead.
If the Queen lives to be 100, the chance is Charles could be bed-ridden ill at that time and William could be a Regent in that case.
Parliament does have the ultimate say. This has been the case since the Glorious Revolution.
Regards, Ivan