A month ago, the Government dodged the issue of how to deal with one of the biggest long-term problems facing the nation – the rapidly rising bill for care of the elderly – with the claim that there was simply no room in the current spending round. Now, however, David Cameron has dramatically changed his mind, agreeing to the principle of a cap on the amount that any one person must pay, regardless of either the level of care or the length of time it is required.

Quite right, too. Last year, around 40,000 people were forced to sell their homes to pay for care. With a room in a care home now costing an average of £26,000 per year, one in four of them faced bills of more than £50,000. One in 100 had to find £100,000 or more.

More troubling still, the problem is set to grow exponentially. In 20 years, the population of over-65s is projected to grow by 50 per cent and the number over the age of 90 is expected to treble. There is no avoiding the fact that, as a country and as individuals, we will need to spend a far greater proportion of our income on support for our declining years.

Politicians, however, have ignored the demographic time-bomb for too long. As a result, we have a muddled system which provides social care only to those who have assets of less than £23,250. For everyone else, the sale of a house – either before or after death – is often the only option, creating enormous anxiety for the elderly, compounded by there being no way to predict the worst-case scenario.

Andrew Dilnot – an economist who led an investigation into the issue last year – described the current system as "nuts". He proposed, instead, that an individual's total care bill should be limited to £35,000, and that those in need should not begin paying unless they had assets of £100,000 or more.

But although politicians of all parties welcomed the report, the Government last month deferred consideration of how the £1.7bn bill for the Dilnot proposals would be paid.

The move was a catastrophic failure of leadership and one that was rightly attacked by charities for the elderly as a betrayal of Britain's older people. The Prime Minister's renewed insistence on finding a solution broadly in line with Mr Dilnot's recommendations is, therefore, welcome. It will not only allay fears of unaffordable costs. By eliminating the prospect of unlimited liability, it will also remove barriers to the development of an insurance market to help defray the risks of more moderate bills.

Big questions remain as to how the plans will work and how they will be funded. It is not clear, for example, whether the controversial idea of care costs paid from the estate after death will form part of the package, and, if so, who will value properties, or how interest rates will be set; local authorities have neither finances nor the expertise to make such a scheme a success. Social changes, such as family break-ups which may result in fewer potential carers, will add to the challenges. And there are already issues over the quality of care, an area which has seen complaints rise by nearly a quarter in the past year alone.

None is insurmountable, but they will require concerted efforts at resolution. Both parties in the Coalition have indicated that they will commit to implementing the Dilnot recommendations, and Labour has also promised its support. But it is now time for politicians across the spectrum finally to live up to their promises. With House of Lords reform abandoned, there is even the time in the legislative programme. If the space was filled with concrete measures to address one of the most pressing issues of modern Britain, the trade-off might almost be worth it.