Huh? From what I recall of the history of English drama, the theaters were closed altogether from 1642 to 1660; Cromwell was Lord Protector from 1653 to 1658.
1642 - The closing of the theatres by Parliament in 1642 is perhaps the best-known fact in the history of English drama.
1660 - Prior to the Restoration period, public English stage performances had been banned for 18 years by a Puritan regime, led by Oliver Cromwell. When theaters re-opened in 1660, it signaled a rebirth of English drama.
You are right. I was wrong.
The banning of theatres (originally a five-year ban) in 1642 occurred when Cromwell was an MP and a Colonel but was not yet a dominent figure.
Actresses of the time were mostly confined to the underground theatre and John Milton approved recitations. Milton loved both Shakespeare and Cromwell and was one of the most powerful Cromwellians to continue living in England after the Restoration without facing trail.
Of course theatre bans were periodic at other times especially during plague spikes.