A report found receptionists carried out intitial checks on patients
A second inquiry is to be held into Stafford Hospital where a health watchdog found "appalling" emergency care led to patients dying needlessly.
Health Secretary Andy Burnham said current and ex-NHS staff would be expected to co-operate with inquiry.
In March the Healthcare Commission said about 400 more people died between 2005 and 2008 there than would be expected.
On Tuesday the Care Quality Commission said there had been progress, but some areas had to be addressed "urgently".
The regulator, the successor to the Healthcare Commission, said mortality rates had been "showing early signs of improvement".
It added it was satisfied Mid Staffordshire NHS Foundation Trust had made an acceptable start in "implementing the systems, resources and people it needs to make the improvements recommended" by its predecessor.
Christine Braithwaite, from the Care Quality Commission, added: "There are still areas which need to be addressed urgently, such as the purchase and use of equipment and more nursing staff."
The commission said people using A&E services reported improvement during the day but less satisfactory care at night.
Burnham denies 'inquiry U-turn'
In March, the Healthcare Commission identified deficiencies at "virtually every stage" of emergency care and said that managers pursued targets to the detriment of patient care.
One of the worst examples of care cited in the watchdog's report was the use of receptionists to carry out initial checks on patients.
The new inquiry will be chaired by Robert Francis QC, who will hear evidence from patients and families and identify lessons for the future, the government said.
The inquiry was announced by the Department of Health as part of a package of measures to tackle "exceptional failures" in foundation trusts.
The government said if the chairman considered it necessary to have the power to require witnesses to attend, the secretary of state would take the necessary steps to ensure this happened.
In a proposed change to the law, the health secretary will be able to ask independent regulator Monitor to remove foundation trust status from a hospital where it had failed and where this was in the best interests of patients.
Mr Burnham said the "overwhelming majority" of foundation trust hospitals were "high performing", but their status must "always be seen as a privilege and not a one-way ticket".
He denied that the government had performed a U-turn following a campaign from relatives of patients at the hospital for a full public inquiry.
The government had previously said there was no need as the Healthcare Commission investigation had been comprehensive.
He added: "This new independent inquiry will give patients and their families the opportunity to present their evidence and ensure that any other lessons are learned without unduly distracting the new management and staff at the hospital from improving services for patients today."
Julie Bailey, from the group Cure The NHS which had campaigned for a public inquiry, said she saw it as "a positive step forward".
She added: "We want to know why this happened to our loved ones? Why nobody listened to us for so long after we told so many people?"
The Foundation Trust Network said its members would "welcome the fact that ministers intend to give power to de-authorise foundation trusts to Monitor".
But it said: "We need to be clear about the way in which Monitor and the Care Quality Commission work together to ensure there is no confusion".
The Conservative MP for Stone in Staffordshire, Bill Cash, said Tuesday's announcement was "a significant step forward".
Last week it was announced Antony Sumara had been appointed as chief executive of Mid Staffordshire NHS Foundation Trust, which looks after Stafford Hospital.
Sir Stephen Moss has been appointed as chairman.
Former chief executive Martin Yeates resigned in March, along with chairman Toni Brisby, before the damning report into the hospital was published.
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