IIRC at the time of their marriage Philip was King of Chile and Naples and Duke of Milan.
It's not impossible but you'd need a PoD somewhat earlier than their OTL marriage. You need to get the common people on side with the Habsburgs and Habsburg wars abroad, so, you'd need some PoD that results in significant Anglo-Spanish victories in France (ie, England gaining territory thanks to Philip). You'd need a less troubled and more fertile Mary and/or Elizabeth. You'd also need to butterfly away the Reformation, so that Philip's Catholicism works in his favour and there's none of the horrid persecution OTL saw under Mary.
What I can see happening is...Mary dies, either leaving the throne contested (threat of civil war), or they have a son, who rules for some years but dies childless. The popular King Philip then steps in and rescues England from civil war, marrying one of the various female heirs (Elizabeth Tudor, Margaret Douglas, Frances Brandon, Jane Grey, &c), legitimizing her rule and restoring peace and the line of succession. His popularity is such that Parliament gladly allows him greater share of power, maybe even the crown matrimonial, or (maybe if other heirs are dead or not-viable) the line of succession in case his second wife's line dies out. (Remember Philip had the superior Lancastrian bloodline to the actual Tudors).
Alternatively, maybe Don Carlos marries a young English lady of the blood, receives crown matrimonial/a certain amount of royal power, he dies childless, civil war, blah blah, King Philip steps in and saves the day, receives the crown together with nice English bride.