Atkins walked out of the deal following changes to the way the education department allocated funding to more than 100 schools in the borough.
However, the council insists it has followed government guidelines by devolving power to individual head teachers.
Strategic director of education and culture Dr Roger Smith said: 'The debate was always about having much more empowerment and more resources at [head teachers'] disposal.
Education secretary Charles Clarke said his objective was to cut specific grant and give councils and teachers more say in how cash was spent.
A spokeswoman for the Department for Education & Skills added: 'Money still gets allocated to council education departments, but it is up to councils to ensure it goes directly to schools.'
However, this policy means Atkins was expected to pitch for work from each individual school so the firm decided to terminate its contract.
Business services managing director Michael Foote said: 'The contractual arrangements have been increasingly financially challenging. We therefore approached the council to request an amicable premature termination of the contract and to allow Southwark LBC and the secretary of state to put alternative arrangements in place.'
Unison national officer Geraldine Reardon said the collapse of the deal highlighted the difficulties inexperienced councils and firms face when negotiating complex PFI contracts.
She added: 'A more experienced company may have pulled out of negotiations much earlier. Running an education service is a lot more complicated than people think and the government has a free-flowing policy which can change at any time, creating genuine problems for the contract.'
The contract was signed in April 2001 after the g overnment intervened following a poor Ofsted report two years earlier. It was expected to last five years, but staff will transfer back to council control while alternative arrangements are put in place.