Pressure is mounting on Health Secretary Andy Burnham as Staffordshire county councillors rejected the new probe announced into the scandal at Stafford Hospital.

The authority is demanding a full public inquiry be held instead.

The county council accused the Government of “pussy-footing around” at a full council meeting yesterday and unanimously voted in favour of urging Mr Burnham to “show true leadership” by calling an immediate full public inquiry.

There are fears the limited terms of reference of the new independent inquiry mean witnesses will not be compelled to give evidence under oath and that parts may be heard in private.

Cabinet member for adults and wellbeing, Matthew Ellis, said: “We’ve now had five of these independent inquiries, all with different but narrow terms of reference in isolation from one another. Another one is not what’s needed.”

Mr Ellis said he would be writing to the chairman of the inquiry, Robert Francis QC, to ask him to shut down the new inquiry.

“I’ll be asking him to open his inquiry and immediately close it with the recommendation that a full public inquiry is the only way to get to the bottom of the scandal of care at Stafford Hospital and Mid-Staffordshire NHS Foundation Trust,” he added.

A damning Healthcare Commission report published in March revealed between 400 and 1,200 more people died than would have been expected at the trust between 2005 and 2008.

Councillor Ellis said: “I must make it crystal clear we’re not attaching any blame to the front-line staff working at the hospital. But we must get to the bottom of the institutionalised problems at Stafford Hospital.”

He added the county council’s own health scrutiny committee should play a “fundamental role” in the inquiry. “The committee needs to have open access and be a fundamental part – to be the eyes and ears of people living in Staffordshire,” he said.

Janet Eagland, the chair of the committee, proposed the motion at yesterday’s meeting which was unanimously agreed by members.

She said: “We’re told the chairman of this inquiry has the power to convert it into a public inquiry if he sees fit. But we do not have detail of how this may happen. I am concerned that this announcement allows the secretary of state to wash his hands of having to make this very important decision himself.

“I urge the secretary of state to show true leadership and call a public inquiry now.”