Tory council leaders across England and Wales have presented a united front with Labour and Lib Dem-run local authorities as they warn the chancellor, George Osborne, that another round of funding cuts would devastate local services and harm the most vulnerable in society.

In a letter to the Observer, council bosses representing every type of local authority in England and Wales, as part of the Tory-controlled Local Government Association (LGA), say they have already had to impose cuts of 40% since 2010 and cannot find more savings without serious consequences for community life and social care, and knock-on effects for the NHS.

Last week Osborne unveiled radical plans for further devolution of powers to English cities, including housing and transport. However, the letter, signed by the leaders of all 375 county, district, unitary and metropolitan councils, as well as London boroughs and Welsh councils, sets the stage for the most serious conflict between central and local government since Osborne launched his austerity drive five years ago.

Following the 7 May local election results, the LGA returned to Conservative control after a year of Labour being the largest party, so the protest is Conservative-led and aimed directly at the new Tory-majority government. In the letter the local authorities say they have already made efficiency savings that have cut services to the bone. “Councils have worked hard to shield residents from the impact of funding cuts. However, efficiencies cannot be remade or buildings resold,” they say.

“Further local government funding reductions over the next five years are not an option. The new government must consider the consequences that further funding cuts, without radical reform of the way public money is spent, will have on the services which bind our communities together and protect the most vulnerable.”

They warn that “vital services, such as collecting bins, filling potholes, maintaining our parks and green spaces, caring for the elderly, would struggle to continue at current levels” and would “result in the unintended consequence of costs passed on to other parts of the public sector, such as the NHS, [which would be] left to pick up the pieces of councils scaling back services”.

The strength of their feeling reflects a sense across local authorities that they are bearing an unfair burden, as ministers try to meet their targets to rein in public spending and slash the deficit.

They add: “If our public services are to survive the next few years, councils need fairer funding and the freedom to pay for them. The public sector has to stop working in silos and join up even more. We need a new settlement for England that devolves decisions about infrastructure, transport, housing, skills and health and social care down to local areas so they can tackle the big issues facing their residents.

“Councils could then ensure elderly and disabled people receive the care they deserve, young people are equipped with skills to find local jobs, desperately needed homes are built, roads are maintained to high standards and every child has a place at a good school.”

Osborne announced plans on Saturday for an emergency budget on 8 July in which he will lay out how he intends to cut £12bn from Britain’s welfare bill and announce a fresh wave of austerity measures. It will be his second budget in less than four months. The chancellor says he wants to make a start delivering on commitments made in the Conservative party manifesto and that his package will be a budget for “working people”.

The Treasury says he will provide details of how the government plans to eliminate the UK’s budget deficit – forecast to be £75bn this year – and run a surplus by the end of the parliament. “On 8 July I am going to take the unusual step of having a second budget of the year – because I don’t want to wait to turn the promises we made in the election into a reality … And I can tell you it will be a budget for working people.”

The Treasury said the budget would address Britain’s poor productivity record, and include plans to create three million new apprenticeships. However, the centrepiece of the package will be a fresh bout of austerity. Provided the economy performs in line with forecasts made by the independent Office for Budget Responsibility, borrowing will be reduced to £41bn in 2016-17 and £14.5bn in 2017-18. By 2018-19, the plan is for the UK to be running a budget surplus of £4bn.

The Conservatives have provided details of how they will find around £1.5bn of savings from the UK’s social security budget but came under pressure from the Institute for Fiscal Studies during the election campaign to explain how they would find the remaining £10.5bn. The IFS said the scale of the overall savings – 10% of the part of the welfare bill not spent on pensioners – would involve the Conservatives looking at child benefit, child tax credit and disability allowances. According to the Treasury, the budget would announce reforms of welfare that would protect the most vulnerable while making sure the system is fair to taxpayers.