In the very broadest of strokes, the reformation continued under Henry's son, Edward VI, who was perhaps groomed by Thomas Cranmer to be more receptive to reform than his father had been. While Henry had seemed rather receptive to reform after his break with the church in Rome and was in communication with Melanchthon in Germany, he ended up insisting (largely after the appointment of Tunstall, a religious conservative, to the Privy Council) on maintaining a church that looked much more like the Roman church than what was seen; for example, he refused to allow the marriage of clergy (an embarassment for the married Cranmer) and affirmed a number of dogmatic points in the Six Articles in a very Roman-leaning way. Henry then vacillated to a significant extent, and there was considerable pressure from parties seeking to expand the reformation and those looking to undo it in the English church.

Under Edward, Cranmer spearheaded the publication of the first Book of Common Prayer and the 42 Articles, which established a much more Protestant doctrine, but these were rescinded by Mary after Edward's death, as Mary reestablished ties with Rome. Reformed bishops were removed from office. Cranmer was forced to recant but then renounced his recantation before his execution.

Upon Mary's death, Elizabeth broke ties with Rome again and the 39 Articles were published, which again established a number of reformed/Lutheran doctrinal positions but rejected a number of extreme doctrines, such as anabaptism. The term often used for the position Elizabeth established is the via media -- the middle road between the Roman church and the extremist reformers and Puritans.

There was some hope on the accession of James on the part of the Puritans that he would support further reform, having been a member of the more reformist Church of Scotland, but he maintained the episcopal structure and via media doctrine of the Church of England, and established a commission to publish an approved common English translation of the Bible.

I find Moorman's "A History of the Church in England" helpful, although it can be dry and is rather too short to give a full treatment of any given period. It is also said to suffer from something of an Anglican bias, in that it argues the position that a peculiarly English Christian tradition predated the Tudors and was simply given independent expression by Henry VIII. I've never found that difficult, due no doubt to my own Anglican bias.

Thank you for your delightful answer.