Atkins Education has asked to end its five-year pound;100 million-plus contract which started in 2001.
Teachers have remained in the council's employment during privatisation and their jobs will be protected. The 350 council staff who transferred to Atkins are expected to be re-employed.
Schools will return to local authority control if terms are agreed between the Department for Education and Skills and the company.
The council will appoint an outside management team to oversee its education service for one year.
One head, who did not want to be named, said: "For two years we have been used as a government experiment which has failed. Atkins should have made the jobs of heads and teachers easier but it made them more difficult."
Schools in difficulty, such as those in special measures which have had most contact with Atkins, are most likely to be affected.
WS Atkins, Atkins Education's parent body, pulled out after budget negotiations broke down. A source said the council wanted to pay it less in 200304 than last year.
Council leader Nick Stanton said: "We were paying everything due under the contract and more on top. This year Atkins was told to pay more to schools."
Southwark was ordered by the Government to hand over the management of education services to a private firm after a second Office for Standards in Education report in 1999. The latest Ofsted report in July 2002 said the LEA was functioning satisfactorily overall, but that some weaknesses remained.