An NHS source told The Telegraph: “It’s impossible to know what we would have done had we been told. However, that would have been the first opportunity for the trust to know that he had lied on his original application form.
“It was an opportunity that should have been there.”
The local trust has launched a review but eight local MPs are calling for a wider public inquiry to examine how he was able to carry out the attacks for so long.
Mr Clark said: “It’s beyond the resources and capability of a local NHS trust.
“The questions that are raised include local ones about how this was allowed to happen.
“But there are also national ones as to whether national policy was good enough, was stringent enough, and whether it could have happened in other hospitals across the country.”
Fuller is facing a whole-life term after admitting to the sexual assault and murders of Ms Knell and Ms Pierce.
He also admitted to 51 other offences, including 44 charges relating to 78 identified victims in two mortuaries, at the former Kent and Sussex Hospital, which closed down in 2011 and the Tunbridge Wells hospital in Pembury, which opened in 2010.