Birmingham city council has announced a further 1,000 job cuts and warned it may soon no longer be able to pay for services such as caring for vulnerable people and rubbish collection unless dramatic changes to funding or the structure of local government are made.

The Labour-controlled council said it would be struggling to fund all statutory services within four years on current projections. The latest job cuts were on top of 7,000 that have already been made over the past three years. The council said it needed to find savings totalling just under £840m between 2010 and 2018, including £120m of cuts in the 2014-15 financial year.

Speaking as he launched a white paper on the proposed budget for next year and longer-term city finances, the council's leader, Sir Albert Bore, said: "Birmingham faces a severe financial crisis. Politicians in Westminster are systematically dismantling services that maintain the very fabric of culture and community here."

It has been a torrid few years for Birmingham. The city council has already shed a third of its workforce since 2010. This year it hit the headlines when a damning serious case review into the murder of two-year-old Keanu Williams found deep problems in children's care and prompted an extraordinary and wide-ranging attack by the chief inspector of Ofsted, Sir Michael Wilshaw, who branded Birmingham a "national disgrace".

At the launch of the white paper, Planning Birmingham's Future and Budget Consultation 2014-15, Bore said an extra £10m had been made available for children's safeguarding services and no jobs would be lost in this area.

But he painted a grim picture for the rest of the decade unless the government helped local authorities to find a new way of working. "These cuts will mean the end of local government as we know it," he said. "But that does not mean the end of local government. We now need to build the new local government that will replace it. We call on the government to make radical changes to the way local services are funded and provided."

One idea is for the creation of a larger single funding pot at the city region level for services provided by the likes of local authorities, health organisations and the Department for Work and Pensions. Bore said this would make savings to the overall public purse by avoiding duplication.

Other ideas suggested in the white paper include transferring services to private operators or community and voluntary organisations and creating new "local hubs" that include, for example, a health centre, library, neighbourhood office, community centre and police station.

"Local government has got to change; we've got to redefine the role of local government," said Bore.

He added that he believed traditional Labour strongholds such as the cities and towns of the Midlands and the north were being disproportionately hit by the Tory-Lib Dem coalition at Westminster.

"Birmingham has been unfairly treated over recent years and the government needs to put that right," he said.

Ian Ward, the deputy leader of the council, added: "By the time we get to 2017-18, if we continue down this road we will struggle to continue to provide statutory services."

The city council is holding a series of public meetings over the next few weeks as part of its consultation on its proposed budget for the next financial year and its longer-term plans.

Joe Morgan, the regional secretary of the union GMB, criticised the council, saying: "The cuts proposed could set Britain's second largest city back decades. It is an absolute disgrace that a Labour-controlled council is letting this happen."