This is a wonderful video of a speech given by Gamal Abdel Nasser in which he recounts a meeting with the General Guide of the Muslim Brotherhood (at the time, probably Hassan al-Hudaibi) in which he tried to patch things up and, as he puts it, "set them in the right direction." He asks them what their demands are. The Guide replies that his first demand is that all women in Egypt be forced to wear the veil.
The interesting thing is that this line generates an uproar of laughter in the audience. One man shouts out, "why doesn't he veil himself."