Henry VIII removed his kingdom from the power of the Vatican, making himself the Supreme Governor. The Queen inherits that position, but she does not have, (or want, I am sure) any power over the ways that services in the Cof E are conducted, or what the congregation does in bed, or any of the Pope's almost supernatural-seeming powers. She is a kind of Chairman of the Board to the bishops and archbishops who run the organisation.
Thanks for that explanation, Elegran.
I rather think that Henry VIII had quite a lot of say in how the Church in England was conducted! But appreciate that his successor doesn't.