Patient safety in the NHS in England is being put at “unacceptably high” risk, with severe staff shortages leaving hospitals, GP surgeries and A&E units struggling to cope with soaring demand, health chiefs have warned.

The health service has hit “breaking point”, the leaders say, with record numbers of patients seeking care.

Nine in 10 NHS chief executives, chairs and directors have reported this week that the pressures on their organisation have become unsustainable. The same proportion is sounding “alarm bells” over staffing, with the lack of doctors, nurses and other health workers putting lives of patients at risk.

Sajid Javid, the health secretary, has come under fire for recently claiming, at a No 10 press conference, that he did not believe the pressure on the NHS was unsustainable.

But the survey of 451 NHS leaders finds the health service already at “tipping point”. The results of the poll, conducted by the NHS Confederation, which represents the healthcare system in England, Wales and Northern Ireland, show that 88% of the leaders think the demands on their organisation are unsustainable, and 87% believe a lack of staffing in the NHS as a whole is putting patient safety and care at risk.

The survey of the most senior executives running hospitals, ambulance services, mental health providers, community services, primary care and integrated care systems comes hours before new performance figures for the NHS in England are due to be published.

The number of people waiting for hospital treatment in England has hit a record high of 5.7 million as the NHS struggles to clear the backlog of care that has been worsened by the pandemic. Updated figures are expected on Thursday.

The greatest areas of concern for NHS leaders are primary care, and urgent and emergency care, according to the survey.

Matthew Taylor, the chief executive of the NHS Confederation, said: “Almost every healthcare leader we’ve spoken to is warning that the NHS is under unsustainable pressure, and they are worried the situation will worsen, as we head into deep midwinter, unless action is taken. They are also sounding alarm bells over risks to patient safety if their services become overwhelmed, on top of a severe workforce crisis.

“The health and social care secretary says the NHS is not under unsustainable pressure, but NHS leaders are clear that we have reached a tipping point. Frontline providers across all parts of the NHS are under intolerable pressure.”

A hospital trust chief executive in the south-east said: “Systems are at breaking point and risk is unacceptably high [for] some cohorts of patients, be that in emergency, primary care, cancer or elective care [or elsewhere]. But where is the honesty and openness about this?”

An ambulance leader revealed that pressures were so severe they were hampering the organisation’s “ability to respond to immediate life-threatening calls” and meant “some patients will die”.

Taylor said that while the NHS was approaching winter with more than 90,000 vacancies, the “number one measure” ministers could take now to stop the NHS plunging into crisis would be providing emergency funding for social care, which had even greater numbers of unfilled jobs.

The Guardian revealed last month that the NHS was facing a mounting beds crisis because care homes with unprecedented staff shortages had to stop taking in patients from hospitals.

Health leaders are trying to free up space in the NHS to tackle the backlog of 5.7 million people – equivalent to almost 10% of the population of England – awaiting treatment. But efforts to speed up the discharge of patients into the community are being hampered by care-worker shortages.

The most endorsed recommendation by health leaders in the NHS Confederation poll was for ministers to provide urgent extra support for social care. This should be targeted at ensuring effective discharge arrangements so that people can live more independently in care homes or in their own homes, health leaders said.

The NHS beds crisis is now so serious that as many as one in five beds in some hospitals are occupied by patients who are medically fit to be discharged, the Guardian was told. In most cases that is because there is no care package available to enable them to leave hospital.

Taylor said the required extra support for social care services should include more money to increase care assistants’ wages to help fill staffing vacancies, and to increase the staff’s fuel allowance so more people could be persuaded back into the sector.

He added: “We welcomed the government’s recent extra investment in the NHS, but we cannot immediately buy our way out of this potential crisis due to the 90,000-plus vacancies in the NHS. It would be better to allocate more immediate funding, from the recent funding settlement, to social care services, as boosting the numbers of care staff will have much greater impact on reducing pressures on hospitals and other parts of the NHS.”