In 2011, Nigel Crisp, former chief executive of the NHS, wrote a forceful book about his experiences entitled 24 Hours to Save the NHS. A book written today would have a similar title: Ten Days to Save the NHS?. In his forthcoming autumn statement, George Osborne may provide an answer to the question.

The NHS has to deal with huge challenges, many the result of decisions taken years ago. For example, the number of funded places for young men and women training in this country as nurses was cut by 12% – 2,500 places – in 2012. The consequent shortage of newly qualified nurses has been filled by people recruited by employment agencies. The cost of agency staff is one of the main reasons for overspending by NHS trusts. In 2014/15, agency staff cost the NHS £1,770m, a year-on-year increase of 29%. The response of NHS managers to the Mid Staffs scandal and the reports on staff shortages headlined by the Care Quality Commission led NHS trusts to step up recruitment before the general election.

Many young doctors took advantage of the special concession extended to overseas students studying medicine to work in the NHS for two years after qualifying. They filled places for junior doctors in hospitals, not least in A&E clinics. In 2012, that tier one concession was revoked and an absurdly high minimum income requirement for skilled non-EU workers was introduced. Some of the vacancies in these emergency facilities have had to be filled by more expensive agency staff.

The third area of inherited expenditure arose from the private finance initiative, contracts entered into by NHS trusts with the private sector for the building of new hospitals and usually paid for over 25 years or more. One of the first, at Darent Valley, cost £80m to build but the total repayment costs amount to £800m. Last year, five trusts went into deficit because of PFI commitments. In the most troubling cases, such as Peterborough and Stamford NHS trust and Barts Health in London, the PFI-related debt goes into the tens of millions – in the case of Barts, £93m.

Not all the challenges are inherited. Pressure on the NHS is likely to increase as winter comes. Jeremy Hunt, the health secretary, has threatened to impose a new contract on junior doctors, prompting strike threats. At a time when many newly qualified British doctors are choosing to work abroad, compelling them to sign a hated contract is unlikely to staunch the flow.

These additional costs come on top of an ageing population, leading to more social care from hard-hit local authorities. The Institute for Fiscal Studies calculates that local government expenditure was cut by 20% in real terms between 2009/10 and 2014/15. Patients unable to get social care locally will turn to the A&E clinics and the hospitals, a challenge the NHS cannot meet. Hospital beds will be blocked by frail patients. A harsh winter could break the back of the NHS.

Facebook Twitter Pinterest George Osborne at last month’s Conservative party conference. Photograph: Suzanne Plunkett/Reuters

There is, however, some prospect for substantial savings from new approaches to medical practice. In 2012, Professor Timothy Briggs, then medical director of the Royal National Orthopaedic hospital, asked the Department of Health to arrange meetings with ministers to allow him to present a radical plan to improve surgical practices in orthopaedics, changes that would save the NHS large sums of money. He was brushed off and offered no access to ministers.

At the time, I was involved in debates in the House of Lords on the health and social care bill. I was impressed by the bold plan proposed by Professor Briggs and asked Earl Howe, then the parliamentary under secretary of state for health, to see him, which he duly did. He was as impressed as I had been and found the money to finance a trial of the project in which a review of elective orthopaedics was undertaken. It proved highly successful, so successful that it has now been extended to all surgical procedures in the health service.

I have spoken to Professor Briggs, who estimates that substantial savings can be made within a few years. But they cannot be achieved in a matter of months. The chancellor’s autumn statement will be announced on 25 November. At present most of the agreed extra expenditure on health, some £8bn, is assumed to be made available in the last two years of this parliament.

Front-loading the extra money could avoid an irreversible collapse. If the NHS, Britain’s single greatest achievement in public services, is to be saved, reconsideration by the chancellor is essential. Surely the prime minister will not want to be seen as the man who presided over the death of the NHS he claims so deeply to care for.

Baroness Williams is a Liberal Democrat peer and a former cabinet minister