To mark the BBC’s coverage of the NHS’s 70th birthday, researchers from the Health Foundation, the Institute for Fiscal Studies, The King’s Fund and the Nuffield Trust have joined forces to shed light on some of the big questions on the NHS.
In their report, What’s the problem with social care, and why do we need to do better? the King’s Fund and Health Foundation have modelled various options for social care funding reform. In comparison to the £1.5bn required to maintain the current (albeit unstable) level of service in 2020/21, it would cost:

£8bn to provide the same level of access to services as in 2009/10.
£5.5bn to introduce a cap on total costs (of £75,000) and a more generous means test (from £23,250 to £100,000). This model, similar to a proposal in the 2017 Conservative party manifesto, would mean including the value of people’s homes in the means test for both residential care and home care.
£7bn to provide free personal care in people’s home, similar to the system in Scotland.

The report points out that although these sums appear small when compared to the amount spent on the NHS, previous proposals such as those produced by the Dilnot Commission and Barker Commission were eventually shelved or ignored on the grounds of cost.
More on NHS funding from The Guardian

NHS and Social care at 70