Charles, the Wikipedia article about the Imperial State Crown has this to say:

"The original St. Edward's Crown, used at the coronation of English monarchs, was considered a holy relic, kept in the saint's shrine at Westminster Abbey, and therefore not worn by sovereigns at any other time. Instead, a "great crown" comprising a circlet of gold with crosses and fleurs-de-lys atop its rim, but without arches (an open crown), was a king's usual headgear on state occasions until the time of Henry V, who is depicted in statuary and illustrations with an "imperial crown", i.e., the great crown with gold arches added (also called a closed crown). Arches were a symbol of sovereignty, and by this point in history, the King of England was being celebrated as rex in regno suo est imperator (an emperor within his own domains), owing obedience to no one but God (unlike some continental rulers, who owed fealty to more powerful kings, or to the Holy Roman Emperor)."

Googling also finds Encyclopedia Britannica entries from old editions that show illustrations of the various kinds of crowns.