Ben Reid, chairman of Shrewsbury and Telford Hospital NHS Trust's board, told a meeting in November that the trust had delayed publishing the July 2017 report from the Royal College of Obstetricians and Gynaecologists.
The trust then sent a delegation of staff to London to persuade the authors to write a more positive addendum regarding the improvements they claimed had been made, before finally publishing them both together a year later.
He told the meeting there had been attempts to "soften" the report's conclusions.
It prompted families to file a formal complaint accusing the trust of “a deliberate and pre-meditated plan to cover-up and water down the significant concerns" contained within the report.
Professor Stephen Powis, NHS England’s national medical director, has now asked the investigation team based at NHS Improvement to look into the "serious concerns" raised.
He says he has advised the trust to ensure it fully cooperates and will discuss the findings with the Care Quality Commission and the Ockenden independent review, which is now looking into 900 cases of alleged poor care at the trust dating back 40 years.
The review was launched by former Health Secretary Jeremy Hunt in 2017 to examine 23 cases, after concerns were raised by families whose babies died shortly after being born in the trust's care.
Richard Stanton, whose newborn daughter Kate Stanton-Davies died in 2009, said the trust had a "toxic culture" and "doesn’t want the truth to come out".
He said: “These are not accidental deaths, these are avoidable deaths and cases of harm.
“People have covered this up in places of authority when they should have been protecting the public.”
Mr Stanton says he wants to see Mr Reid step down and someone else take charge.
He added: “He’s not fit for purpose to be running that trust at chairman level.
“There needs to be someone else to come in, and in fact he should actually just resign and show his actions were so poor, so ill-judged that that would be the right thing to do.”
SaTH, which runs Royal Shrewsbury Hospital and Princess Royal Hospital in Telford, says it is working with NHS Improvement on the investigation.
During a debate in the House of Commons on Wednesday, Nadine Dorries, Parliamentary Under-Secretary of State for Health and Social Care, revealed that 900 cases are now under review by the independent inquiry into maternity care at the trust.
Maternity expert Donna Ockenden, who is leading the review, has urged any other families with concerns to come forward.
The team can be contacted by emailing firstname.lastname@example.org or call 01243 786993.
A leaked report into the inquiry last year revealed a catalogue of concerns and that dozens of babies and mothers are thought to have died or been left disabled due to poor care at the trust.