Until now, the government had no say in church record keeping, and parish registers as we know them today had not been kept. Accounts of the common man were few and far between to this point, since few owned land or left personal property of note to be disposed of in probate court. Keep in mind that serfdom was still dying, and the concept of freedom had not truly taken root for most subjects. The idea of caring about, let alone documenting, the life of the common man was still a relatively new and forward-thinking concept in England.
Therefore it comes as little surprise to see that it took parish priests a few years to adopt the habit of maintaining orderly records of births, marriages, and deaths of all parishioners, even after being ordered to do so twice. But slowly the habit caught on, facilitated by the implementation of annual Bishop's Transcripts in 1598. For these three centuries, from 1531 to 1837, when Civil Registration was implemented, parish records are the essential font of genealogical information pertaining to the common man.
So, setting aside the turmoil and strife which stemmed from the Catholic and Protestant disagreements, let's take a moment to thank Henry VIII for implementing a system whereby we can hope to trace our ancestors possibly as far back as the day when England dared to defy Rome. Although for most of us who descend from former serfs and peasants, our story ends (or begins) there, at least we have some records to shed light on the past. Without Henry VIII, we might not even have that.
Example parish register
For further reading about English Parish Records and related topics: