The history of the Kingdom of England's main predecessor state, the Kingdom of Wessex, dips back into legendary territory (do historians agree on whether or not King Cerdic even existed, or if he did, whether or not he actually founded a "kingdom" in Wessex in 519 CE?). As such, I'm limiting the scope of the question to after England as a whole was formed.
By "successor states", I am referring to the Kingdom of Great Britain and the United Kingdom. I know England was and is a distinct part of those, but I didn't want the existence of, say, a Scottish monarch to somehow be counted as England being ruled by a "foreign" power.
So focusing specifically on the Kingdom of England in the Middle Ages.... From 1016-1043 England was ruled by Scandinavian kings, specifically Danish kings, who often ruled England alongside their holdings in the kingdoms of Denmark and Norway. These rulers dominated across much of the North Sea and frequently traveled between the realms. In 1066, William the Conqueror, Duke of Normandy (northern France) wrested control of the kingdom from the Anglo-Saxon nobility and for the next generation rule of England wasn't even the primary concern of the nominal kings of England, who were much more concerned with their French holdings and fighting their siblings over control.
Whether these periods constitute "foreign rule" I think is a matter of debate, and relies on modern conceptions of nationhood/identity which I can go into if you'd like, but these two times are times when the Kingdom of England was held by a person who we, modern Anglo-phone people, would not really consider an English person, though the issue is somewhat contentious in some cases. I'm not going to touch on later developments such as the Acts of Union between Scotland and England or the Glorious Revolution as those lie outside of my wheelhouse.