The RCPCH was told about the doctors' suspicions of Letby and went ahead with the inspection anyway. From a HR / legal perspective, I agree that was the wrong choice. But as some of the inspection team commented at the Thirlwall Inquiry, they considered it important to examine the unit urgently to ensure that it was functioning safely. Their findings around understaffing, irregular ward rounds, significant skills gaps, failings in emergency transport etc were valid whether or not Letby or anyone else was deliberately harming babies.
Jane Hawdon wasn't told there had been allegations against anyone before conducting her review, but she was told about them afterwards. At that point, she didn't in any way suggest that her review didn't stand. Again, the failings in care were evidenced in the notes she had examined. She responded by giving advice on how to handle any bruised egos among the consultants, advising that the downgrade of the unit shouldn't be called a downgrade.
Since the trial, the consultants have pushed a narrative suggesting management exposed children to further harm by ignoring them. If you look at the facts as supported by contemporary evidence, Letby was removed from the ward within a week of the consultants suggesting they feared deliberate harm (but acknowledging they had no evidence). The hospital undertook a thorough investigation, and Letby never returned to the ward. The coroner was informed of the accusations and the investigations. When the consultants refused to accept the outcome of the investigations, the hospital contacted the police as they requested.
I do think that informing the police from the outset would have been the best course of action, but that would not have affected any of the children Letby was charged with harming. It will be very interesting to see how the police justify any claims about criminal negligence manslaughter if that's the road they try to go down.