South London Healthcare, a merger of three hospital trusts, is spending 14% of its income on repayments to a private finance initiative (PFI).
The government says the financial problems are caused by a PFI scheme signed off under Labour.
Labour says there are wider financial pressures in the NHS, and PFI also delivered many new hospitals.
The government could appoint an administrator within weeks, but in the meantime the trust’s hospitals will continue to run as normal.
The move raises the prospect that other trusts could follow in its wake.
There are another 20 trusts that have declared themselves financially unsustainable in their current form.
Work has already started to rectify their problems and therefore wholesale dissolving is considered unlikely.
However, the move over South London Healthcare does act as a warning that the government is prepared to use the measure, which was made possible by legislation Labour introduced in 2009.
‘Deep challenges’ South London Healthcare amalgamated the Princess Royal University Hospital in Orpington, Queen Mary’s Hospital in Sidcup, and the Queen Elizabeth Hospital in Woolwich in 2009.
When the three hospitals became one organisation they inherited a large debt - mainly from the private finance initiative (PFI) that had been used for the buildings at Orpington and Woolwich.
Last year it finished £69m in deficit on a turnover of £424m.
As well as struggling financially, the trust also has some of the longest waiting times for operations, and longer-than-average waits in A&E. However, it does have low infection and death rates.
If a decision was made to break up the trust, it would not necessarily mean the closure of all services. Another more successful NHS organisation or private provider could end up taking on some.
But for that to happen, there would need to be a formal process of review and consultation.
While South London Healthcare Trust is carrying a heavy burden of PFI repayments, there are more complex factors behind the financial pressures facing some other trusts.
Wake-up call Andrew Haldenby, from the think tank Reform, told the BBC that some other PFI schemes had delivered good hospitals and good value for taxpayers. But he warned that difficult decisions about the numbers of hospitals in England could not be postponed.
“One in five hospitals are in real financial difficulty. Every hospital - even if it is in the black right now - needs to be looking really hard at this. Although we are talking about South London today, every NHS Chief Exec needs to be looking at this today.”
Any decision about South London Healthcare would need to be signed off by Health Secretary Andrew Lansley and reported to Parliament.
In a letter to the trust, Mr Lansley said: “A central objective for all providers is to ensure they deliver high-quality services to patients that are clinically and financially sustainable for the long term.
“I recognise that South London Healthcare NHS Trust faces deep and long-standing challenges, some of which are not of its own making.
“Nonetheless, there must be a point when these problems, however they have arisen, are tackled. I believe we are almost at this point.”
Mike Farrar, head of the NHS Confederation, which represents trusts, said: “We welcome this decision. The NHS can’t go on with short-term fixes to financial problems.
“That might mean some tough decisions, but hopefully will deliver financial sustainability in the long term.”
Chris Streather, chief executive of South London Healthcare, said patients could be assured that services would continue as normal during this process.
He added: “There is a huge gap in our financial plan in order for us to become viable in the long term and this intervention if it solves that problem which it is designed to do is absolutely welcome and will be helpful.”
The trust expects the discussions to come to a conclusion in the second week of July, when a decision on whether to put it in administration will be taken by the secretary of state. However, it will probably be October by the time the review is completed.
But Labour accused the government of “losing its grip” on NHS finances and wasting billions of pounds on an NHS reorganisation which is “opposed by patients and health professionals”.
Shadow chancellor Ed Balls said he accepted that some early PFI deals were poor value for money but defended the investment in hospitals.
“The big picture is up till 1997 we had no new hospitals being built at all and in constituencies across the country people were crying out for decent healthcare. We built tens and tens of new hospitals.”
But Health Minister Simon Burns said it was time for “decisive action” instead of “sweeping this under the carpet.”
Along with South London Healthcare, the other 20 trusts identified by the government as facing financial difficulties are: Newham University Hospital, Barking, Havering and Redbridge, North Cumbria Hospital, Surrey and Sussex Healthcare, Epsom and St Helier Hospitals, Trafford Healthcare, Scarborough and North East Yorkshire, Winchester and Eastleigh, George Eliot Hospital, Nuffield Orthopaedic Centre, Oxford Learning Disability Trust, Whipps Cross Hospital, North Middlesex Hospital, Ealing Hospital, Hinchingbrooke Hospital, North West London Hospitals, Weston Area Health, Great Western Ambulance Service, Dartford and Gravesham and Suffolk Mental Health Partnership.
Published by By Branwen Jeffreys and Nick Triggle BBC News On 26 June 2012 Last updated at 14:27 See http://www.bbc.co.uk/news/health-18584968