Older and vulnerable people could stop receiving vital help to get out of bed, washed and dressed, because the underfunding of social care has become so severe, councils have warned.

Leaders of 370 local authorities in England and Wales fear that some councils are finding it so hard to provide the right level of support they could face a high court legal challenge for breaking the law.

The Local Government Association said care visits could become shorter, carers could face greater strain and more people could be trapped in hospitals, making NHS services even busier as a result. The LGA estimates that there will be a £2.6bn gap by 2020 between the amount of money social care services need and their budgets.

Cllr Izzi Seccombe, the chair of the LGA community wellbeing board, said: “The intentions and the spirit of the [2014] Care Act that aims to help people to live well and independently are in grave danger of falling apart and failing, unless new finding is announced by government for adult social care.”

The act, which came into effect in 2015, was intended to ensure that councils provided help with basic everyday tasks to anyone who was struggling to undertake at least one of them on their own, because of a physical or mental impairment. But the purpose of the legislation is at risk because councils cannot afford to meet demand, the LGA told the Treasury in its submission ahead of the budget in March.

Only 8% of council directors of adult social care said they were confident that they could fulfil their full duties under the act in 2017-18.

Barbara Keeley, the shadow social care minister, said: “It is deeply worrying that councils are now having to spell out the risks that this lack of funding is causing. We should not tolerate the fact that growing levels of basic needs are going unmet, care visits are shorter and there is increased strain on unpaid family carers.”

A government spokesman said: “Local authorities have a duty to implement new rights introduced in the [2014] Care Act and while many are already providing high-quality social care services, we will continue to challenge and support those not currently doing so.

“We have provided councils up to £7.6bn of dedicated funding for social care over the course of this parliament, significant investment to ensure that vulnerable people get affordable and dignified care as our population ages.”