Local authorities should be given the freedom to impose higher council taxes to help cope with the unprecedented funding crisis facing social care services after a near decade of austerity, the Tory chair of the Local Government Association has said.

James Jamieson urged ministers to inject billions of pounds into adult social care and give councils more control of local health services to protect elderly and disabled people and give them the support they needed. “It is a measure of a good society how well it treats it most vulnerable,” said the councillor.

Reflecting increasing concern over the impact of the reductions, he called for major extra investment in children’s social care, a reversal of cuts to Sure Start-style early-years family support services and a review of special educational needs services funding.

His comments reflect a growing cross-party consensus at local level that national government has little grasp how continuing austerity cuts are hurting local communities and putting people at risk. Last month, Jamieson’s Tory predecessor, Lord Porter, warned that vulnerable people would die because of social care cuts.

There is little confidence that the government will be in a position to deliver its promised three-year spending review this autumn, effectively imposing a further year of austerity on town halls and forcing them to plan for service cuts and staff redundancies they had hoped would be unnecessary.

The LGA warned earlier on Tuesday that the deteriorating outlook for council finances would see a fifth of authorities forced to impose drastic controls on spending this year to avoid insolvency, while a third of councils would struggle to deliver statutory services within three years.

Jamieson, in his inaugural speech at the LGA annual conference in Bournemouth, said the council tax referendum cap, introduced by the Tory-Liberal Democrat coalition in 2012 and currently set at 2.99%, ought to be abolished. “Residents should be given the choice; if they want to pay more for extra services, why can’t they?”

He said that councils in England had lost 60p out of every £1 of central government funding since 2010, while the number of new child protection investigations had doubled, there had been a 56% increase in homelessness and the number of older people aged over 85 had increased by a third.

The communities secretary, James Brokenshire, said in his speech to the LGA that he recognised councils’ uncertainty over future funding, adding: “It is right that we look at the challenges and opportunities you face, and the funding you are currently relying on, including for social care, when we consider what a sustainable settlement looks like for local government for the coming years.”

Meanwhile, a survey of council chiefs found nearly half expect that Brexit will damage their local economies by reducing exports and overseas investment. This would critically reduce council income from business rates at a time when they were already struggling to maintain the quality and breadth of core services.

PWC’s annual survey of council leaders, chief executives and finance directors revealed that more than half believed that some authorities would get into serious financial difficulty or fail to deliver core services at some point over the next year.

A PWC survey of 2,000 UK users of council services found that 67% were concerned about cuts on their community, up from 61% a year ago; 77% said they or their family had been impacted by cuts; and 51% opposed the need for cuts, up from 48% in 2018.

Councils must hold a referendum if they wish to raise council tax beyond the 2.99% limit. No local authority has taken up the option. In January, Northamptonshire county council was given special dispensation by ministers to raise council tax by an extra 2%, raising £6m, to aid its recovery from insolvency. Similar requests from other councils have been turned down.