Kingdom Church in Camberwell Station Road was taken to court by Southwark Council after the local authority said it had received a "flood of complaints".
The church's leader, Bishop Climate Wiseman, said he will appeal the fine and there had been no complaints since a new roof was installed.
He told the Southwark News: "It is a big fine and we will be appealing against it. I do not deny that we made some noise - we did. But we have spent nearly £10,000 reducing the noise. And I was out of the country so could not go to court.
"We are based is an industrial area. But there are new flats and they complain. The flats were meant to be offices but they became houses. People could hear it, especially in summer when they open their windows."
According to the church's website it has to hold prayer services at 3am because "it is a well-known time that witchcraft and negative elements begin to work".
It adds: "While the witches are busy working their witchcraft you are getting the wisdom of God concerning their demonic operations."
The church was found guilty of two charges under Section 80 of the Environmental Protection Act 1980.
Councillor Michael Situ, Southwark Council cabinet member for communities and safety, told the newspaper: "We would have preferred to settle this matter out of court, but unfortunately our attempts to work with the church leaders were ignored.
"We hope the penalty helps to remind both the leaders, and the wider community, anti-social behaviour of any kind will not be tolerated and wrongdoers will be made to pay one way or another."