Select Education plans to officially launch an out-of-school division offering the service next month, and is already in talks with 15 authorities and 25 headteachers about the scheme.
The supply agency says the project will help headteachers cut staff workload, add to their school's income, and meet growing demands from parents and the Government that they provide a longer school day.
Select would profit from the Government and lottery funding available to run the projects, and would pay classroom assistants and qualified teachers similar hourly rates to those they would receive for working during the school day. A primary teacher could earn around pound;50 for a three-hour, after-school club.
Select spokesman David Rose said there was plenty of funding available for out-of-school-hours schemes, such as pound;191 million given by the lottery's New Opportunities Fund in the past three years, but headteachers were often too busy to organise the activities themselves.
The company would give schools a few thousand pounds each year for the use of their premises, he said, and staff at the schools could be involved if they needed extra money.
The company has been trialling part of the scheme in the south London borough of Bexley, where it ran holiday projects for four to 14-year-olds at three primary schools during the summer.
Jeff Holman, of the National Association of Head Teachers' education department, said he expected many headteachers would be tempted by Select's new service, if they could ensure that all staff involved were competent and qualified.
"If they are providing something which will take the burden off schools, that's fine," he said.
"But without proper supervision and staffing, a homework club could create more problems for a school than it would solve. Heads would need to be satisfied they were not going to receive complaints the following day."