Time is defined as from the death of the previous holder and the accession of the next.
The one I have gotten thus far.
Elizabeth I (1603) to Elizabeth II (1952)=349 years
Edward VI (1553) to Edward VII (1901)=348 years
Charles II (1685) to Charles III ((2022)=337 years.
The longest might be:
William II Rufus (1100) to William III of Orange (1689) = 589 years
After that I think you got the next three.
Edward the Confessor (1066) to Edward I (1272) = 206 years
ETA: Hah! First! 
nm … ninja’d
The time between John I and John II is infinite (or about 800 years), considering there hasn’t been a John II and isn’t likely to be one.
The gap between Stephen I and Stephen II beats that.
Well if we’re going down that road, I haven’t seen many princes named Æthelstan lately…
Yep, that one seems to be the tops of those that are repeats. (can’t fail to observe BTW that the accesion of two out of the four Williams so far involved landing from the continent with an army)
Here we also run into this curiosity of how they seem to have set the official English ordinals to start with the Normans, so it is Longshanks who gets the “I” attached to him.
I keep thinking of William and Mary as well William and Mary. Even though strictly speaking they were William III and Mary II.
It’s probably gonna be awhile before there’s an Arthur II. 
It’s also observed that of the 4 William, only the last is known by his regnal number. The first three are “the Conqueror”, “Rufus”, “of Orange” or “&Mary”*.
As aside is the College of William and Mary after the joint sovereigns or some other couple name Bill and May.
After Mary’s death, William was known as William III; see the statute citation for the Act of Settlement:
Established under letters patent issued by authority of the royal couple. So they sucked up honored them in naming the school.