Older people in England’s most deprived areas are twice as likely to lack the help they need for basic acts, like using the toilet or taking medicine, compared with those in the richest neighbourhoods, according to figures that expose gross inequalities in access to social care.

The official analysis is another sign that years of cuts have damaged the ability of councils in poor areas to meet the growing demand for care, potentially putting significant pressure on the NHS. It comes on the back of the crisis over social care that is still unresolved. There have been a series of warnings about a multibillion-pound funding black hole and increasingly severe consequences for the health service.

A third of men aged 65 and over in the most deprived areas (33%) have an unmet need for at least one so-called “activity of daily living”, such as washing their face and hands or getting out of bed. In the least deprived areas the figure falls to 15%. Meanwhile, 42% of women over 65 in the most deprived areas have an unmet need for at least one such activity, compared with 22% of their counterparts in the richest areas.

The inequalities were exposed in the latest data from the official Health Survey for England. It used information on income, employment, education, health, crime, housing and living environment to find the most and least deprived neighbourhoods. Local authorities with the highest proportion of deprived neighbourhoods are in Middlesbrough, Knowsley, Hull, Liverpool and Manchester.

A series of factors have led to poor areas finding themselves at the sharp end of the care crisis. Demand for help is higher in more deprived areas, while the councils catering for them have suffered the most from central government cuts and are the least able to raise extra funds.

The knock-on effects for the NHS see elderly patients end up in hospital unnecessarily after accidents at home, , while they cannot be discharged unless they have adequate community care in place. Among men, 30% in the poorest third of households needed help with an activity of daily living (ADL), compared with 14% in the highest income group. Among women, the need for such help was 30% among the poorest third and 20% in the highest third.

There is a growing army of unpaid helpers, such as family and friends, propping up the system. Around two-thirds of adults aged 65 and over, who had received help for daily activities in the past month, had only received this from unpaid helpers, the figures revealed.

Izzi Seccombe, the chair of the LGA’s community wellbeing board, predicts a £2.3bn funding gap for care by 2020. Photograph: None

Spending on adult social care by local authorities fell from £18.4bn in 2009-10 to just under £17bn in 2015-16, according to the respected King’s Fund. It represents a real-terms cut of 8%. It estimates there will be an estimated social care funding gap of £2.1bn by 2019-20.

While an extra £2bn was provided for social care over two years, a huge gap remains after the latest budget failed to address the issue. Theresa May was forced to abandon plans to ask the elderly to help pay for social care through the value of their homes, after it was blamed for contributing to her disastrous election result. The government has promised to bring forward some new proposals by the summer, but many Tory MPs and Conservative-run councils are desperate for faster action.

Ministers have dropped plans to put a cap on care costs by 2020 – a measure proposed by Sir Andrew Dilnot’s review of social care and backed by David Cameron when he was prime minister.

Izzi Seccombe, the Tory chair of the Local Government Association’s community wellbeing board, said: “Social care need is greater in more deprived areas and this, in turn, places those councils under significant financial pressures. Allowing councils to increase council tax to pay for social care, while helpful in some areas, is of limited use in poorer areas because their weaker tax base means they are less able to raise funds.

“In more deprived areas there is also likely to be a higher number of people who rely on councils to pay for their care. This, in turn, puts even more pressure on the local authority.

“If we are to bridge the inequality gap in social care, we need long-term sustainable funding for the sector. It was hugely disappointing that the chancellor found money for the NHS but nothing for adult social care in the autumn budget. We estimate adult social care faces an annual funding gap of £2.3bn by 2020.”

Simon Bottery, from the King’s Fund, said: “We know that need will be higher in the most deprived areas – people get ill earlier and have higher levels of disability, and carry that through into social care need.

“We also know that the councils that have the greater need to spend are, on average, raising less money through the precept [earmarked for funding social care].”