Barnet council has recommended Capita as its preferred bidder for a £32m-a-year contract to run its back-office services.
The 10-year deal would see the outsourcing company operate London Borough of Barnet's new support and customer service organisation.
If successfully implemented, the contract would make Capita responsible for a wide range of council services, including the call centre, human resources and IT. A total of 514 jobs would transfer to the private-sector firm.
The council says that the decade-long, £320m contract will guarantee savings of £120m. The proposals are part of the One Barnet Programme, an initiative intended to save the local authority money following a £43m cut in funding from central government.
But the controversial plans to hand the running of council services over to a private company are opposed by a group called the Barnet Alliance for Public Services, which argues that the Capita deal could end up costing the taxpayer more, rather than less.
"The benefits they are boasting have an equal likelihood of great cost to the borough of Barnet," campaigner Barbara Jacobson told the BBC.
"I find it hard to believe that they can guarantee these kind of savings over 10 years when we don't know what's going to happen to the economy, and I am worried about the effects of transferring these jobs to Capita on the local economy," she added.
The group argues that similar outsourcing schemes intended to cut costs, such as SouthWest One, have suffered high rates of failure. But Barnet Council insists that the move is needed in order to improve services and prevent redundancies.
"The alternative to the contract we are proposing is to make much bigger cuts in frontline services and jobs over the next couple of years," said leader of Barnet Council, councillor Richard Cornelius.
A final decision about the proposal will be made at a cabinet council meeting on 6 December.
Successful leaders are infusing analytics throughout their organisations to drive smarter decisions, enable faster actions and optimise outcomes
Focus on cost efficiency, simplicity, performance, scalability and future-readiness when architecting your data protection strategy