NHS Improvement said restrictions on agency staff spending had delivered millions of pounds in savings.
In the first three months of this year, NHS trusts ran up deficits totalling £461 million - some £5 million less than expected, NHS Improvement said.
It said that 185 trusts had met their financial commitments but 29 have not. A small number have so far failed to agree financial targets with NHS Improvement.
The organisation says a "small number" of hospitals are failing to deliver a high quality service in the face of increasing demand.
During the three months, there were some 300,000 more attendances at emergency departments than a year ago - a total of 5.34 million, it reported.
Chief executive Jim Mackey said: “This is a crucial year for the NHS. Today’s results have demonstrated that providers are up for the challenge and are starting to get a grip on their finances.
“The performance data is more disappointing. While the majority of NHS trusts are meeting the extra demand from patients and still delivering a high quality service, a small group are letting the side down. We need to support them up their game so they provide the services patients rely on.”
But British Medical Association chair Dr Mark Porter said: "Our health service is already buckling under pressure now, and I dread to think what will happen to the quality of patient care with any future slowdowns of funding as predicted in this report.
“We’re still seeing hospitals and GP surgeries at breaking point, waiting times too high, crushing pressure on mental health services and cuts to the public health budget. The majority of trusts are in the red and the NHS doesn’t have enough staff or resources to meet demands.
“Patients deserve more than sticking plaster solutions to what is an acute financial crisis."
Chris Hopson, chief executive of NHS Providers, warned that trusts would struggle to maintain their financial improvements.
He said: "The £1.8 billion support for provider deficits and the first sensible tariff efficiency targets in years are having the desired effect."
But he added: "There is now a clear and widening gap between what the NHS is required to deliver and the funding available.
“However, any sense of optimism must be tempered by what finance directors are telling us. Nearly four in ten finance directors are saying they will be unable to sustain this level of performance and expect their trust’s position to worsen over the rest of the year. They are not confident because of the sheer scale of the challenge they face but also because they do not want to miss their first quarter numbers and then lose access to the extra money.
“These findings show the strain NHS trusts are operating under. There is now a clear and widening gap between what the NHS is required to deliver and the funding available. This will only get worse as overall funding increases drop from next year."
He added: "In reality, we have only just kept our heads above water because we have transferred the investment intended to fund long term transformation into reducing the deficit that the majority of NHS trusts face."
The service at Stafford Hospital - now known as County Hospital, Stafford - lacks sufficient staff with the right levels of paediatric and anaesthetic training, it was announced.
Managers said children could no longer be taken to the hospital as emergencies.
The service was created in May last year following the reorganisation of services in Staffordshire - which in turn followed the inquiry into problems at the Stafford hospital.
Yesterday University Hospitals of North Midlands said the service had been found to be "unviable" and that safety concerns had been raised in a report from the West Midlands Quality Review Service.
A spokesman said: "Senior clinicians have now spoken with staff in detail, and carried out a thorough review of the training received as well as both competence and confidence levels around the issues highlighted.
"It has become apparent that concerns raised by WMQRS cannot be addressed in the short-term, which is why we have temporarily suspended the service."
Dr Anthea Mowat, from the British Medical Association, said: “This is yet another example of patients being failed because the government doesn’t appear to have a solution to a workforce crisis in many parts of the NHS."
The Royal College of Paediatrics and Child Health said the paediatric workforce is at "breaking point."
Vice-president Dr David Evans said: “If we are to prevent similar cases like the one of Stafford hospital today, decision makers must take urgent action. In the short term we need to see an increase to trainee and consultant numbers and better advanced planning of emergency and non-emergency rotas.
“In the long term more care needs to be delivered in the community by multi-disciplinary teams of paediatricians, GPs and nurses.
"And with children accounting for around a quarter of a typical GP’s workload, GPs deserve far greater support to help equip them with the skills needed to manage a child’s health needs safely at home and prevent unnecessary hospital admission, where possible.”
The National Institute for Health and Care Excellence launched a consultation on approving the use of software called HeartFlow FFRCT.
The software creates 3D images of blood vessels from standard cardiac CT scans.
NICE says it could save £214 a patient compared with standard diagnostic tests and help avoid invasive investigations and treatment. It would be used for patients with stable recent chest pain and with an intermediate risk of heart disease.
About 36,000 patients a year could benefit.
Professor Carole Longson, from NICE, said: "Accurately diagnosing the cause of chest pain is important for ensuring that the affected person receives appropriate care and treatment.
“The preliminary view of the independent committee is that HeartFlow FFR CT is innovative and using it in practice may simplify the series of tests used to diagnose the condition.
"Based on the evidence that the committee considered, they concluded that the device is highly accurate in diagnosing coronary artery disease, and that it has the potential to reduce the need for invasive coronary investigations – which is good news for the patient."
A major research project shows that damage to stem cells is a key factor in the development of cancer. This could come from random mutations, accumulated with age, or external damage.
But researchers found that local DNA damage to organs often enables damaged stem cells to trigger cancer.
They say this local damage, often the result of environmental factors, such as tobacco, "wakes up" stem cells.
The study also found that stem cells in adults are much more vulnerable to mutating than are those in children.
Researchers at Cambridge University, UK, and the St Jude Children's Research Hospital, Memphis, Tennessee, USA, reported their findings in the journal Cell.
Researcher Professor Richard Gilbertson brought the project from Tennessee to Cambridge.
He said: “We can now say that cancer most likely starts in stem cells but is not just down to bad luck. The development of cancer involves a perfect storm of stem cells containing DNA mistakes that are replicating in response to damage or wear and tear.
“Although stem cells can sometimes go wrong by chance, our research shows that things in our environment that lead to more DNA mistakes or that damage organs, causing these stem cells to divide, increases the chances of the ‘perfect storm’ brewing. That’s why behaviours like smoking or UV exposure raise the risk of developing cancer.
“Our work also shows why some types of cancer are more common than others, with tumours more likely to develop in organs with lots of replicating stem cells, for example the bowel.
“We hope finding out more about the way in which cancer develops will help us, and other scientists around the world, develop new ways to prevent and treat cancer.”
He added: “An argument has raged across the scientific community for some years now. Some say cancer is bad luck because mutations arise by chance in stem cells, while others argue environmental carcinogens are more important.
"This disagreement has arisen largely from the use of different mathematical models to look at existing human cancer and stem cell data, from which it is extremely difficult to tease out the impact of individual factors. Therefore, we tested these opinions in actual experimental models that looked at the individual components that might drive cancer.”
Liqin Zhu, et al. Multi-organ mapping of cancer risk. Cell 25 August 2016; doi: 10.1016/j.cell.2016.07.045 [abstract]