The deputy leader of Birmingham City Council has admitted it is possible its £120 million-a-year Service Birmingham contract could be torn up.

The outsourcing contracts with Capita have come under increasing scrutiny as the council looks to close a £460 million funding gap over the next four years.

Under the agreements Capita has provided computer systems and IT support, a call centre, and council tax revenue collection among other services.

The deal was first signed in 2006 and during the first six years the city council paid Capita just short of £1 billion. It has been criticised for being poor value for money to the taxpayer. The deal runs until 2020 and it has been claimed early cancellation would be too costly.

But deputy leader Ian Ward (Lab, Shard End) said they are now weighing up this option. “We have asked officers to work out the best deal we can get on reducing the costs of these contracts, and what the financial benefits are,” he said.

“We are asking what it would cost us to end the contract early, and then what it would cost to re-establish our own in-house IT department and call centre.

“We need to work those costs out over the life of the contract and work out the best deal for the taxpayer.”

In a swipe at backbench critics who have called for the deal to be scrapped overnight he said: “If we cancelled it tomorrow we would need to have something in place.”

Last week Labour council leader Sir Albert Bore announced the local authority is negotiating a £20 million reduction on the core IT contract with Capita, which costs the city council between £50 million and £60 million a year.

While other contracts relating to one-off projects, the call centre and other services are also being looked at for cuts.

Capita sparked controversy in 2011 when it attempted to export Service Birmingham IT developer jobs to India. The jobs were returned to the city at a cost of £1 million a year to the council.

The Labour administration has been threatening to cut the costs of the deal since it took over in 2012. The Capita-led company made £58,400-a-day pre-tax profits last year – despite the council’s struggling finances.