The government has revealed the calculations behind its offer of free personal care at home - and admitted it does not know whether the benefits of the policy outweigh the costs.

In an impact assessment published alongside the short bill, which amends the 2003 Community Care Act, Department of Health officials state: “Due to uncertainties in certain components of estimated benefits… it is not possible to say whether the net benefits of this intervention definitely outweigh the costs.

“However… it seems plausible that the net benefits are substantial.”

The impact assessment reveals that – as LGC predicted – the free care offer will be restricted to a small proportion of the group of service users currently defined as having “critical” needs under the Fair Access to Care Services system.

To qualify, service users will need to be in the critical group and also have difficulty performing four “activities of daily living” – another measurement used by health professionals to gauge a person’s ability to perform basic tasks.

The government estimates that 443,818 people fall into this category.

But the impact assessment acknowledges that data on the number of service users registered as FACS critical is not collected centrally.

LGC revealed that councils able to predict increases in demand at critical level were anticipating a 10 per cent increase over the next five years on average.

The government has launched a consultation alongside the bill with a closing date next February.

Shadow health minister Stephen O’Brien described the bill as “politically motivated policy worked out on the back of an envelope”.

He said: “Many pensioners will be deeply disappointed that the Labour government is failing to think seriously about how it will offer good long term care for our ageing population.”