The English Drama's performances began in the church. As the popularity of the productions rose, the churches were unable to hold the masses and the productions began to spill out onto the church grounds. This became a problem. The people who came to watch the plays had to cram together in order to see the productions. This became a problem when they began to step upon the graves of the church grounds.
As the audience became bigger, the plays moved to the streets in front of the churches. As this happened, non-followers began to become interested in the plays and improvise parts. As the productions moved further and further from the church, because of their popularity, the priests began to have less and less control over what was being produced. Eventually, many plays moved to taverns.
Given the priests no longer had say in the productions, given their movement from the church, plays began to possess things which the Church would not support (drunkenness and sexuality). The Church even banned plays during the Medieval Period.
Therefore, the English Drama became secular based upon the Church's inability to control the productions given they no longer were produced under the watchful eye of the Church. Since the Church no longer had power over the plays (given they had moved off of church grounds), plays were able to include material not religiously appropriate.
English drama actually is originated in church. That is the reason it is said that the cradle of English drama is church. In the beginning the priests used to enact some scenes from the Bible in between the holy mass in order to get the attention of the congregation. Latter on this enactment has come out of the alter but still it continued to take the religious themes life the miracles of Jesus and the lives of the saints etc. Later on it came out of the churches and the theme has changed into secular. Through these process the English drama got secularised.