I have a different theory. England cannot win a penalty shootout. They fear PKs more than any other nation.
This shortcoming has more powerful effect than simply losing actual penalty shootouts as they have many times u know Italia 90 Euro 96 and so on. It is rooted in the collective psychology. It also causes stress towards the end of regulation or extra time when they are tied and seek a winner to avoid this fate, or even when they r one goal up but their opponents are pressing hard within the last tens mins for an equalizer. At these times their composure and form goes to pieces and they concede unnecessarily.
It's not even lack of confidence in their keepers. Usually England has at least decent keepers. It's the PK takers who collapse....