Two acts of the 1559 parliament did the work. The Act of Supremacy restored the crown's authority over the church but styled the queen Supreme Governor rather than Supreme Head, a wording that answered the objection that no woman, and arguably no layperson, could head a church. The Act of Uniformity imposed a single Book of Common Prayer and made attendance at the parish church compulsory, with a fine for staying away.
The prayer book was the finer instrument of the two. At the administration of communion it joins the words of the 1549 book, which say that the body of Christ preserve thy body and soul, to those of the 1552 book, which tell the communicant to take and eat in remembrance. A worshipper who believed in a real presence and a worshipper who believed in a memorial could both say amen to the same sentence, and that was the intention. The Thirty Nine Articles, settled in the following decade, are Protestant in doctrine, while the structure was left standing: bishops, cathedrals, church courts and a good deal of the ceremony. The result is a church defined more by a shared liturgy than by a shared belief, which is much of the reason Anglicanism has the shape it has.
Two details show how deliberately the ambiguity was kept. The rubric on ornaments left church furnishings at the standard of the second year of Edward VI, which meant that what a parish actually looked like depended on who was reading the sentence. And the fine for absence from church was set low at first and raised sharply only in the 1580s, once Catholic loyalty had become a security question rather than a religious one.