Social care has remained one of Westminster’s longest-running unresolved problems. Successive governments have promised reform, only for plans to be delayed, watered down or abandoned as the financial implications became clearer.
Mr Burnham now appears determined to put the issue back at the centre of Labour’s long-term political offer.
His proposal would represent a major change from the current system, under which people can face substantial costs if they require long-term care and have assets or income above the relevant thresholds.
The Prime Minister’s argument is that the existing model already imposes a significant financial burden on families. Someone who develops substantial care needs can potentially see years of savings disappear, while homeowners may fear that the value of their property will ultimately be consumed by care costs.
Mr Burnham believes that makes the current system not only expensive, but fundamentally unfair.
His comparison with the United States was deliberately striking. He argued that, just as medical bills can create severe financial consequences for vulnerable Americans, the British social care system can leave families facing devastating costs at precisely the point when they are already dealing with illness, disability or old age.
The political attraction of reform is therefore obvious.
A promise of publicly funded social care could appeal strongly to older voters and families worried about future care bills. It could also give Labour a defining policy ambition beyond the immediate pressures of the Government’s day-to-day programme.
But there is an obvious problem.
Free care is not actually free.
The bill must ultimately be paid either through taxation, government borrowing or reductions in other areas of public spending. Mr Burnham’s statement that the system would operate on the basis that “everyone contributes” is likely to be interpreted as a warning that higher taxes could form part of the eventual settlement.
That immediately raises questions about which taxes could increase.
The Prime Minister did not specify whether future increases could involve income tax, National Insurance, wealth-related taxation, inheritance tax or another form of levy.
Nor did he provide a detailed timetable for introducing the reforms.
Those omissions are politically significant.
Labour would need to convince voters that any additional taxation was proportionate to the benefits being offered. It would also need to explain how the system would protect people on modest incomes while ensuring that wealthier households contribute a fair share.
There is an additional challenge surrounding intergenerational fairness.
Younger workers already face high housing costs, rising living expenses and a significant tax burden. Asking them to finance a more generous social care system for an ageing population could become politically contentious unless they can see a direct benefit for themselves and their families.
At the same time, older voters are an increasingly important electoral constituency.
Many pensioners have spent decades paying taxes and contributing to the economy. They may argue that publicly funded care is simply another part of the welfare state they have already helped finance.
Mr Burnham’s task will be to turn those competing arguments into a single political proposition.
The Prime Minister has already acknowledged that the current Labour manifesto makes it difficult to introduce his preferred reforms during the present Parliament.
That means the next general election could become the decisive moment.
Rather than attempting to introduce the full system immediately, Labour could campaign on a detailed promise and seek a fresh mandate from voters.
This would allow the party to explain the costs before implementation and potentially reduce accusations that ministers were introducing a major tax increase without electoral approval.
However, announcing tax rises before an election is never straightforward.
Opposition parties would almost certainly attempt to portray the proposal as another Labour tax grab. Conservatives and Reform UK could argue that families are already struggling with the cost of living and cannot afford another major increase in taxation.
Business groups could also question whether additional payroll or income taxes would weaken economic growth.
Labour would therefore need to demonstrate that the long-term economic benefits of social care reform outweigh the initial fiscal cost.
There is an economic argument in favour of greater investment.
A dysfunctional social care system can have consequences beyond elderly and disabled people themselves. When care arrangements collapse, relatives may be forced to reduce their working hours or leave employment altogether to look after family members.
That can reduce household incomes, shrink the workforce and increase pressure on the NHS.
Hospitals can also become overcrowded when patients who are medically ready to leave cannot be discharged because suitable social care arrangements are unavailable.
Supporters of reform argue that a better-funded system could therefore prevent some costs from simply being transferred elsewhere in the public sector.
This is likely to be one of Mr Burnham’s strongest arguments.
He can say that Britain is already paying for social care, but doing so in a fragmented and often financially painful way. The question, in his view, is whether the country should continue allowing individual families to absorb the greatest costs or create a national system in which the burden is shared.
The difficult part will be establishing exactly what “free social care” means.
Would every form of care be covered?
Would people receive free residential care as well as support in their own homes?
Would there be income or wealth limits?
Would accommodation costs remain separate?
Would individuals with substantial assets still contribute something?
These details could determine whether the policy becomes a popular flagship reform or an expensive political liability.
Mr Burnham’s personal motivation may also make the issue more significant.
He referred openly to the death of his father and acknowledged that entering Downing Street while dealing with the final stage of his father’s life had been difficult.
That experience could shape his determination to reform a system that has frustrated governments for decades.
But personal conviction will not be enough.
A national social care programme would require detailed legislation, long-term funding and a workforce capable of delivering the additional services.
Britain already faces shortages in parts of the care sector, with providers struggling to recruit and retain workers. Any expansion of publicly funded care could increase demand for staff dramatically.
Labour would therefore need to address wages, training, immigration and working conditions within the sector.
The financial model would be equally important.
If the Government ultimately proposes higher taxation, ministers will have to publish credible estimates showing how much additional revenue would be raised and how that money would be allocated.
Mr Burnham’s rejection of the £18 billion annual figure will also attract scrutiny. By saying the cost is “not that high”, he has created an expectation that the eventual numbers will be substantially lower.
Opposition MPs will be waiting to challenge that calculation.
The Prime Minister may also face resistance within his own party.
Some Labour MPs could support universal social care in principle while opposing the tax increases needed to finance it. Others may argue that the Government should prioritise the NHS, housing or wages before committing billions to a new entitlement.
That makes the policy one of the biggest potential tests of Mr Burnham’s leadership.
The Prime Minister has effectively acknowledged that the present Parliament may not provide the political or fiscal room to deliver the transformation he wants.
But by promising to take the issue to voters at the next election, he has placed social care firmly on Labour’s future agenda.
The coming years will reveal whether the public is willing to accept higher taxes in exchange for protection against potentially devastating care costs.
For Mr Burnham, that may ultimately be the central argument: Britain can continue with a system in which families risk losing their savings and homes when care needs become severe, or it can build a national model in which the cost is shared across society.
Either way, there will be a bill.
The political battle will be over who pays it.