I have heard that Thomas Cromwell convinced Henry VIII to institute the keeping of these registers, after seeing the practice during a tour of Europe. It took many parishes a long time (and the threat of fines) to comply. What was in it for the king, and why was there so much local resistance to the idea?
The parish registers were introduced mainly because Thomas Cromwell had found that they were in common use in the rest of Europe and according to the sources cited by the related wikipedia article, they expressed the desire of the central government to have better knowledge of the population of the country.
The 1538 Act requiring parishes to keep these registers was not initially very popular as many thought that it would create a new way for the King to tax his people, however no tax was attached to these records.