The number of people in the UK aged 85 or older who require round-the-clock help to eat, dress, wash and go to the toilet will almost double over the next 20 years, research has suggested, highlighting the explosion in social care needs.

An estimated 446,000 of over-85s will have “high dependency” care needs by 2035, up from 233,000 in 2015, and equivalent to 10% of all men and 20% of all women aged 85 and over, according to a new study.

Overall, more than 1 million people aged 65 or over will require intensive social care assistance by 2035, up from 783,000 in 2015, it predicted, with increasing numbers of people living into old age with multiple long-term conditions.

Those who have dementia and at least two other major health conditions, such as obesity or diabetes, will double over the next two decades, it estimated, suggesting an extra 500,000 people will need complex forms of care.

The study said health and social care services must adapt to the unprecedented needs of an older population with complex care needs, and warned the state should not rely on family carers as a sustainable solution to the problem.

Unpaid care delivered by adult children of older people was unlikely to keep up with demand, it said. Although more spouses care for partners in old age, many were likely to be living with disabilities themselves. The extension of the retirement age would reduce the pool of informal and unpaid carers.

“These forces will unite to add further stress to social care budgets that help people to maintain independence within the community or fund long-term care needs,” the study concluded.

There has been growing concern over the cost of providing care for older and disabled adults. Spending on social care in English councils has shrunk by £7bn since 2010, and provision was “on the verge of collapse” in some areas, according to local authorities. Councils have said they face a £3.5bn adult social care funding gap by 2025.

Although the government has promised a green paper on social care funding would be published in the autumn, there have been fears that this may come too late as councils prepared to make cuts to social care services to help stave off financial collapse.

The modelling by researchers at the University of Newcastle and the London School of Economics, and published in the Lancet journal, comes against a backdrop of a rapid ageing UK population. About 14.5 million people would be aged 65 or over by 2035, up 50% from 9.7 million in 2015.

By 2035, of the 65-and-over cohort, an estimated 1,065,000 people would be classed as high dependency, 562,000 as medium dependency, and 3,904,000 as low dependency. The remaining 8,918,000 would have no care needs.

High dependency has been defined as needing 24-hour care, medium dependency as needing help every day at regular times and low dependency as requiring care less than daily and being looked after by family and friends.

The study highlighted different trends for men and women, with the latter likely to experience higher levels of care dependency than their male counterparts by 2035, and fewer years of later life spent free of care needs.

Prof Carol Jagger of Newcastle university’s Institute for Ageing, and a co-author of the Lancet paper, said the gender differences highlighted the importance of focusing on disabling long-term conditions such as arthritis that were more common in women than men.

Simon Bottery, a senior fellow in social care at the King’s Fund thinktank, said: “This study is further evidence of the scale of pressure building up on social care services from an ageing population, which is compounded by growing demand from working age adults with disabilities.”

He added: “Above all, it highlights the urgency of the challenge to reform social care and provide support to growing numbers of people in a way that is fairer and provides better quality but is also affordable in future.”

A Department of Health and Social Care spokesperson said: “In the autumn we will set out our plans to reform adult social care alongside our long-term plan for the NHS, so we can address the challenge of our growing ageing population head on and ensure services are sustainable for the future.”

The Labour councillor Nick Forbes, who is the senior vice chair of the Local Government Association, said: “This report is a further warning of the crisis in adult social care and the urgent need to plug the immediate funding gap and find a long-term solution on how we pay for it and improve people’s independence and wellbeing.”