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Only 17.7% of NHS trusts were given a 'good' rating for their culture of reporting safety concerns, according to figures on the new government web page devoted to patient safety.
The majority of trusts (61.7%) were rated 'OK', while 20.6% were described as "poor" at reporting safety issues such as understaffing on wards.
A Department of Health spokeswoman made clear that a 'poor' rating' did not mean a deliberate 'cover-up' but could be down to "many reasons".
Health Secretary Jeremy Hunt has told ITV News he is "very proud" that NHS hospitals are now publishing staffing levels in every ward on a monthly basis.
A new web page allows patients to hold their local hospital to account by looking at performance indicators.
The measure also means from next year patients will be able to compare staffing levels at different hospitals.
Mr Hunt said publishing more safety data was an "absolutely critical learning point" for the health service following the scandal involving Mid Staffordshire NHS Trust.
One in five NHS trusts may not be being open and honest about the numbers of patient safety incidents that occur in their hospitals, health officials have said.
Twenty per cent of acute NHS trusts in England have been flagged by health officials for under-reporting patient safety incidents, including events that cause severe harm or even death.
A new tool is being unveiled by the Department of Health (DH) and NHS England which enables the public to see how well their hospital is performing on key safety measures.
The new safety website shows that there are "concerns" about incident reporting at one in five acute trusts, a DH spokeswoman said.
Concerns are raised when a trust may not be reporting enough incidents, not reporting these events often enough or where staff feel that the organisation is not responding to incident reports as well as they could, she said.
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