A second whistleblower has come forward to claim that the head of the National Health Service ignored written warnings about failings in a hospital trust which is being investigated for persistently high death rates.

David Bowles, the former chairman of United Lincolnshire Hospitals Trust (ULHT), said he sent a letter in July 2009 to the chief executive of the NHS, Sir David Nicholson, warning that patients could die there because managers were being forced to meet unrealistic targets. He claimed Nicholson failed to investigate the detailed allegations properly.

Bowles's letter emerged as Gary Walker, the former chief executive of ULHT, defied a gagging order to say that he also warned Nicholson about safety issues in 2009, but Nicholson was "not interested in patient safety".

The Lincolnshire trust is one of 14 under investigation over high death rates.

The intervention of Bowles will increase pressure on Nicholson, who has faced increasing demands to step down in the wake of the findings of the inquiry into Mid Staffordshire Hospital Trust.

It comes as Jeremy Hunt, the health secretary, warned senior NHS executives on Friday that there would be consequences if they had wrongly gagged Walker for speaking out about patient safety.

Bowles says he left his job in 2009 after being threatened with suspension when he refused to commit his organisation to meeting national waiting targets. He said he was being put under immense pressure to meet the targets and to sack Walker, both of which he says he resisted.

"I was put under pressure by NHS bureaucrats to force Gary Walker to leave, but I refused because he was doing a good job of shielding the organisation under relentless pressure to put targets first.

"I wrote to Nicholson in the hope that the full weight of my concerns may be taken seriously," he said.

Bowles, who has worked in the public sector for 30 years, including eight years running local authorities, said: "My letter focused on a senior person in the organisation who I thought was failing to comply with codes to put patient safety first. But the subsequent investigation was no more than a whitewash. It did not look at the safety issues I raised and did not look at the breaches of two codes of conduct for payment by results.

"The allegations were serious – I actually referred to the possibility of becoming another mid-Staffordshire hospital calamity – but the inquiry did not look at safety or the breaches of the codes," he said.

He sent the letter in July 2009, before he or Walker had left their jobs.

In the letter, seen by the Guardian, Bowles wrote that a senior person in the NHS hierarchy had resorted to bullying. He asked Nicholson to investigate his claims that the same person had demanded an assurance that non-emergency, 18-week targets would be met "in a manner which could be construed as an attempt to bully me and my trust into becoming a Mid Staffordshire and so put patient safety at risk".

Walker was paid £500,000 as part of a package agreed in settlement of his unfair dismissal claim after he was removed as chief executive of the trust. This week he broke his silence, ignoring an email from NHS-funded lawyers ordering him to respect the terms of the gagging order.

Walker said the trust came under such heavy pressure from increasing demand for treatment that he wanted to abandon the NHS-wide target that patients arriving in A&E should be treated within four hours. He claims he was overruled by Dame Barbara Hakin, the then head of the NHS's East Midlands strategic health authority, who is now a senior figure on the new NHS commissioning board, of which Nicholson will be chief executive.

Speaking to the BBC, Hunt said he was concerned that Walker appeared to have been "leaned on" and has written to Paul Richardson, chairman of the trust, to tell him it is not an acceptable way to behave when an NHS manager raises concerns about patient safety.

"I don't think this is acceptable, I think it is the wrong thing to do," he said. "I don't want to make a judgment about the truth or otherwise about what Gary Walker said. Obviously there are very, very serious allegations."

Stephen Dorrell, the chair of the health select committee, has called on the Department of Health to ensure that no action is taken against Walker because he broke the gagging order to speak about patient concerns.

Before taking control of the NHS, Nicholson ran the health authority responsible for supervising Stafford between August 2005 and April 2006. His tenure there came during a four-year period in which between 400 and 1,200 patients died due to a catalogue of failings and appalling standards of care at Mid Staffordshire NHS trust.

A Department of Health spokesperson said that the allegations raised by Bowles and Walker were examined properly by an independent review commissioned by Nicholson and concluded that there were no immediate concerns for patient safety.

"Allegations of this nature are taken extremely seriously. The review concluded there was no evidence whatsoever to back the claims and a summary of the review's findings and Sir David's response were published at the time," she said.

"However, the review did confirm that there appeared to be a lack of strategic direction at the Trust and that clinical governance arrangements were weak and action was taken to tackle this," she added.