The Care Quality Commission's (CQC) new report into the state of health and care across England shows that the system is in a fragile state, they added.
Niall Dickson, chief executive of the NHS Confederation, which represents organisations across the healthcare system, said: "It would be a tragedy if the NHS's 70th birthday was remembered as the year England's care system collapsed, but today's report reveals real concerns that mental health and social care services are not sustainable.
"Contracts are being handed back leaving more individuals at risk.
"Let no-one misunderstand what is being said here - the health and care system is managing well, with some improvements in safety, but its future is precarious. And one in eight older people are not getting the help they need.
"Today's report is unequivocal - the quality of services is in a fragile state as the system strains to treat and support more older people with complex conditions."
Professor John Appleby, director of research at the Nuffield Trust, said: "Today's report shows that although most NHS patients still receive good and safe care, the system as a whole is struggling to cope.
"The CQC's warnings must be seen in the context of the unsustainable financial squeeze. The NHS ended last year with an underlying deficit of £3.7 billion and faces an even greater challenge this year.
"If the response to this problem is to try to exert more grip and push harder from Whitehall, it will fail: at this stage staff and leaders can't work much harder.
"We need supportive leadership which puts the emphasis on working together to tackle difficult changes.
"Perhaps the most worrying parts of this report touch on social care for older people. One in eight are not receiving the care that they need in the community, and costs have already been pushed so low that companies are giving up contracts.
"The future funding and organisation of social care is becoming one of the greatest unresolved policy issues of our time, and action on this is now an important priority."
Margaret Willcox, president of the Association of Directors of Adult Social Services, said: "The fact that nearly four in five adult social care services were rated 'good' and many others have improved is testament to the dedication of care staff working under significant and continuing pressures, although we recognise that more needs to be done.
"However, with councils overspending on adult social care budgets, contracts being handed back, providers closing, councils being fined for delayed transfers of care and potentially facing crippling back pay costs for sleep-in shifts, and the sector struggling to recruit and retain staff, the future is bleak for adult social care.
"While the extra £2 billion funding for adult social care is welcome, this is only short-term.
"Without a long-term, sustainable solution for adult social care, there will be worrying consequences for the fragile care market, the NHS and, most importantly, for older and disabled people, their families and carers who need and deserve good, reliable and personal care."
The older people's charity Independent Age expressed concern over the "shrinking" number of nursing home beds - a reduction of 4,000 in two years.
Charity chief executive Janet Morrison said: "The Green Paper promised at the Budget in March has yet to materialise but the clock is ticking and as yet the Government seems no closer to producing a long-term solution for social care fit for purpose for our ageing population."
Andrew McCracken from National Voices, the coalition of 160 health and care charities, said: "The way services provide care is outdated and often fails people with long-term conditions, despite the fact they account for 70% of NHS spending.
"People's needs don't neatly fall into organisational boxes and services must be better co-ordinated."
The British Medical Association warned that the health system was "one bad winter away from a crisis".
Dr Chaand Nagpaul, chairman of council at the doctors' union, said: "It is worrying that almost one in four acute hospital services and almost a quarter of mental health services are having their performance affected by lack of resources, system pressures and chronic underfunding.
"Now is not the time to rest on our laurels - A&E targets still aren't being met, the number of people waiting more than 10 weeks for routine surgery is the highest it's been in nine years and waits of a year or more are the second highest since 2012.
"The average waiting time for a GP appointment has hit two weeks, and many surgeries closed altogether last year.
"Failures within the social care system are also having a considerable knock-on effect on an already stretched and underfunded NHS.
"We are just one bad winter away from another crisis in our health system."
Jonathan Ashworth, shadow health secretary, said: "The NHS is now running at full stretch with hospitals full to unsafe levels, and ongoing problems in staffing and recruitment which Tory ministers have failed to grasp.
"The Government must step in and give our health and care system the resources needed to provide the best possible care."
Izzi Seccombe, chairwoman of the Local Government Association's Community Wellbeing Board, said: "Social care faces a perfect storm, and the CQC report is yet another timely warning from a key part of the sector of the need to resolve the short and long-term future of care as an urgent priority."
Unison's head of health Sara Gorton said: "The pressures on staff are reaching a point where the well-being of NHS employees and patients is in jeopardy.
"We can't continue to ignore the impact that seven years of working in an underfunded NHS is having on health workers and the services they provide."
Ruth Thorlby, assistant director of policy at the Health Foundation, said: "We need an integrated, national approach to health and social care to address the concerns the report raises, to achieve better health and health care for everyone.
"The goodwill and hard work of the NHS's workforce will not alone solve the problems in the wider system that are resulting in poor care.
"The additional £2 billion made available by the Chancellor in the spring budget was a welcome acknowledgement of the pressure the adult social care sector is under. What is now required is a long-term sustainable solution for the future funding and quality of adult social care. As a start, clarity from Government on what progress is being made would be helpful."