There was no "conversion" to the Church of England, as such, because initially Henry VIII in 1534 simply declared himself head of the church IN England. At first, this was not conceived of as a different religion in any way except for rejecting the authority of the pope over that of the king. There certainly were people in England who wanted to see changes made in a more "protestant" direction, including the Archbishop of Canterbury, Thomas Cranmer, but they didn't make much headway under Henry VIII because he was basically quite traditional in orientation. He saw himself as simply reforming some of the more serious abuses in the Church that the popes had been unwilling or unable to address. The only part of his reforms that really looked a lot like the Reformation was the dissolution of the monasteries Henry authorized. However, this was very much a top-down measure to put more money into the royal coffers under the pretext that monasteries had largely become so corrupt as to be beyond possibility of reform. For the average parishioner, not much changed during Henry VIII's reign.

A big shift really came after Henry VIII's death and the succession of his weak and short-lived son Edward VI in 1547. Thomas Cranmer finally had a pretty free hand to put through many changes in doctrine and practice that were similar to changes that had been made in continental protestantism, like instituting the English-language Book of Common Prayer.

Many of the changes under both Henry VIII and Edward VI were resisted in various ways. Usually, resistance was more clandestine in the form of, for instance, hiding relics or altar furnishings from monasteries that were supposed to be sold or destroyed. In other cases, resistance was open and widespread, as with the "Prayer Book Revolt" in Devon and Cornwall in 1549. The more mandated reforms actually interfered with the traditional religious practices of ordinary people (as opposed to, say, doctrinal changes about the exact nature of the Eucharist), the more resistance they seemed to have generated. But, as mentioned, most of the reforms didn't affect average parishioners all that much. The clergy were affected a lot more.

Under Edward's half-sister Mary, of course, many of these reforms were temporarily rolled back. Under her successor Elizabeth I, the crown was again considered to be superior to the papacy and most of the reforms were re-implemented. However, Elizabeth was wise enough to recognize that a lot of the population was still deeply divided over reform issues. Her attitude was also very similar to her father's; she didn't support the more extreme reformers and preferred a more traditional style of worship. She tried to steer the most moderate course possible between the two extremes but probably had to concede more to the reforming side than she wanted to. All priests and other clerics were required to swear an oath recognizing her as head of the church, and they would lose their positions if they failed to do so. Eventually in 1593, the Recusancy Acts were passed, which imposed various types of fines and penalties for not attending official Church of England religious services.

These remained in force until 1650, but, as you might imagine, the number of people prosecuted as recusants was undoubtedly much lower than the actual number who, in private, considered themselves to be Catholic. Often times, only the adult males of a pro-Catholic family would attend, since they were the only ones liable to prosecution, while women and children attended Catholic masses held in secret. Prominent recusant families hid Catholic priests and helped them clandestinely travel in England.

On the accession of James I in 1603, many recusants hoped their situation would improve, but they were very disappointed when he didn't prove very sympathetic. This disappointment played a significant role in the 1605 Gunpowder Plot in which Catholic conspirators planned to blow up Parliament, James I with it. Naturally, James' policy towards recusants became much more severe after this incident and even more strict legislation was passed in 1606. However, he didn't actively pursue even his own courtiers who were known to be crypto-Catholic so long as they took an oath recognizing his supremacy over the pope and were discreet.

As the seventeenth century progressed under James I's successors, the question of religion became ever-more bound up in politics. To be Catholic virtually meant, in popular imagination, to be at least open to, if not actually involved in, plots to overthrow or murder the king and/or Parliament with the help of foreign Catholic rulers in order to re-institute Catholicism. Reforms continued to proceed in gradual and piecemeal fashion, and the costs of being openly Catholic were high, especially for great families (and of course, priests!) It's therefore difficult to really define who was Catholic and who was not during this period. A person could only be definitively proven a Catholic if he was an ordained priest, refused to take the oath of supremacy, or refused to attend church. It's impossible to know how many people had strongly Catholic sympathies or were crypto-Catholics but still went to church or even took the oath. And we have not even talked about Puritans, who thought the reforms of the church should go much, much further and were also subject to prosecution even though they officially counted as Church of England. So, it's complicated.

Sources:

Eamon Duffy, The Stripping of the Altars, 1992

Antonia Fraser, Faith and Treason: The Story of the Gunpowder Plot, 1997

Ronald Hutton, The Rise and Fall of Merry England, 1994