A leading London hospital trust is expected to record an annual deficit of between £180m and £191m – the biggest overspend in NHS history, the Guardian can reveal.

King’s College hospital trust believes it overshot its projected £146m deficit for 2018-19 by a further £34m-£45m after experiencing a series of setbacks, documents seen by the Guardian show.

The trust is struggling with the most serious financial problems in the NHS as a result of a private finance initiative (PFI) contract, high use of agency staff to cover its chronic lack of nurses, and being fined for missing the four-hour A&E target. The 2013 takeover by King’s of the Princess Royal university hospital (PRUH) in Orpington, Kent, has also increased its costs while it is paid less than other nearby hospitals for providing certain types of care.

It has found it impossible to balance its books for several years as the government’s policy since 2010 of limiting the NHS to annual budget rises of just 1% a year, at a time when demand for care has been rising, has pushed many hospitals into the red.

Drastic budget overruns led to the trust being placed in “financial special measures” in December 2017 and the departure of most of its leadership team, including the then chair, Lord Kerslake, the former head of the civil service.

King’s posted a deficit of almost £132m in 2017-18 – which until now was the largest ever seen – and £48.6m the year before. But last year’s record overspend of £180m-£191m represents a major worsening in its already precarious finances.

Papers circulated to the trust’s senior managers say: “King’s started the 2018-19 financial year with a deficit control total of £146m.” However, they then detail how that projected deficit has risen by at least £34m as a result of delays to its new critical care unit (£4m), failure to hit its savings target (£8m), and loss of expected income because of “poor operational performance” – its inability to meet targets for A&E care and planned operations.

The papers say: “We have experienced further one-offs not foreseen in the original budget of £17m, taking the expected in-year deficit to £180m. We have submitted business cases which, if not approved by [the NHS regulator] NHS Improvement, would increase the in-year deficit to £191m.”

King’s is also grappling with severe staff shortages, according to papers submitted to its board’s most recent meeting. For example, 26.3% of nursing posts in acute and emergency care at the Princess Royal hospital are vacant, as are 12.4% of such posts in its children’s care unit. The nurse vacancy rate in A&E and acute medicine at King’s itself, in Camberwell in south London, is not as bad, having recently fallen from 11.2% to 6.5%. But it still has serious nurse shortages in cancer care (19.4%), children’s care (15.4%) and operating theatres (12%).

“Much of the NHS is in the red but the deficit figures at King’s are in a completely different league”, said Sara Gorton, head of health at the union Unison.

“Such huge and sustained pressures on budgets are having a real impact on staff and patients across the hospital. Massive gaps in staffing mean sky-high agency bills, making it harder than ever for the trust to get back on an even keel, while demand on services is continually growing.”

Jude Diggins, the Royal College of Nursing’s London regional director, said the problems at King’s illustrated the NHS’s worsening lack of staff.

“The situation here is reflective of the chronic shortage of nurses across the health service. It is particularly worrying that trusts, despite best efforts, are struggling to fill the gaps in vital areas of care like cancer, A&E and children’s services,” she said.

“The effect of the nursing vacancies, of which there are around 40,000 across the NHS in England alone, should be treated as a national crisis which if left untended to will do serious damage to patient care.”

NHS trusts in England had not managed to balance their books since 2012-13, said Anita Charlesworth, the director of research and economics at the Health Foundation charity. “The NHS has been trying to manage these problems through short-term fixes such as loans to support trusts in difficulty, raids on capital budgets and growing waiting lists. But it’s clear this approach is not working and in many cases the gap between spending pressures and the funding available is widening,” she added.

A spokesperson for King’s said: “Our current financial forecast is higher than that planned this time last year. However, over the past year, a number of changes have been implemented that will enable the trust to improve its productivity and stabilise its longer-term stability. Despite the financial challenges, the trust continues to deliver excellent, high-quality care and services to patients.

“Following a number of successful recruitment drives in the last year, King’s has cut its nursing vacancy by half to 7.3% – one of the lowest nursing vacancies rates in London. Additionally, a number of recent appointments have been made in areas with higher clinical vacancy rates, such as the PRUH [Princess Royal] emergency department.”