English plays were moved from production in churches to production in inns for a couple different reasons.
First, churches were relatively limited in space. As the interest in the plays produced in the churches began to grow, the church, itself, became unable to accommodate the growing number of people. The only accommodations the church could make was to move the productions outside of the church. This brought about new problems. Some of the sacred grounds of the church, namely the graves, were being desecrated by people standing on the graves of the deceased.
As the number of people grew, the productions flowed over onto street corners and streets. Given that the productions were moving farther and farther from the church, the church's control of the plays lessened. Eventually, those who were not church members became involved in the productions, and the productions became more secular in nature.
Second, in 1210, Pope Innocent III decided to ban drama from the churches. The overwhelming secular nature of the plays (mostly the drunkenness and lewd behavior) was not appropriate for the House of God. By the 14th century, the Church had banned drama on lands belonging to the Church altogether.
The themes of many of the plays were inappropriate for taking place on church lands. While the beginning of plays performed mirrored sermons (regarding the fall of man and his subsequent redemption), people began to tire of hearing the same things over and over again. Plays had changed, and the people who desired to watch them had changed as well. Churches were no longer appropriate for the dramas which the people desired.