Jeremy Hunt is understood to be considering creating a “beefed-up” ombudsman to handle NHS whistleblowing cases and end the culture of silence in the health service.

The health secretary has also said that he is open to holding a Leveson-style public inquiry into the system after hearing stinging criticism of NHS trusts and health unions.

Yesterday Mr Hunt and Simon Stevens, the head of the NHS, met in London with six whistleblowers who have won the support of senior backbenchers on both sides of the Commons in their campaign for an inquiry and fresh investigations into their cases.

Edwin Jesudason, a spokesman for the six and a leading paediatrician, said that Mr Hunt had set out the idea of a powerful ombudsman that could look at the concerns raised by NHS staff about serious failings in patient care.

At present a few cases are handled each year by the parliamentary and health service ombudsman (PHSO), which investigates complaints against the NHS but has been subjected to strong criticism by several MPs.

“[Mr Hunt’s] thought was to have a system where if you had a concern it would go straight up to them and they could certify whether it was genuine whistleblowing,” Mr Jesudason said.

“We told him in no uncertain terms that unless there’s a more basic reform the system will be gamed. The trusts and the unions will carry on giving an account that’s basically untrue and that can suppress the truth from coming out.”

Mr Hunt and Mr Stevens were said to have been stunned when the whistleblowers attacked the NHS unions for failing to support them and warned that no lasting change would be possible without a full public inquiry.

“They know there’s a problem, they just don’t know how much they need to do to deal with it,” Mr Jesudason said.

One whistleblower who attended the summit reacted angrily after the health secretary ruled out intervening in her case on the eve of the meeting. Mr Hunt’s aides initially insisted that he was keeping all options open, but on Monday he said that he did not have the power to help.

“I am not able to get involved in local decisions about the employment of individual NHS staff, as those decisions are a matter for the particular NHS employer, the employee and, in some cases, the employment tribunal,” he wrote in a letter to Sharmila Chowdhury, a radiographer who lost her job after blowing the whistle on alleged moonlighting at her trust.

However, he promised to arrange a meeting between Ms Chowdhury and the independent government body that looks after NHS trusts to “discuss your options for the future”.

Mrs Chowdhury, 54, who has developed cancer and risks losing her home after a protracted employment tribunal against her trust, said that Mr Hunt’s refusal to get involved was “outrageous”.

Sir Brian Jarman, emeritus professor of public health at Imperial College, London and one of the country’s leading NHS policy experts, said the problem was that no single authority wanted to take responsibility for looking after whistleblowers.

“The department of health says it has no powers to intervene in individual cases, but I’m not sure who does intervene in individual cases,” he said. “The situation for whistleblowers seems to be a bit like that for second-level patient complaints [those not received at the hospital]: no organisation is clearly responsible for resolving all individual cases.”

He said that only a public inquiry could ensure that whistleblowers were treated fairly in future.

“Although there is probably a feeling of ‘inquiry fatigue’ at the department of health, I think the only way we would get to the bottom of this would be by a public inquiry into whistleblowing in the NHS,” he said. “It could cover the question of reopening historic cases, but it seems to me only fair that historic cases should be reopened.”

The department of health declined to respond to what they said was a “private meeting”. Later in the day, Mr Hunt tweeted: “Had an interesting and informative meeting with NHS whistleblowers today -the culture in our NHS is changing, but there’s much to do.”