Detectives have identified 78 out of 99 of his victims.
Fuller pleaded guilty to murdering Wendy Knell, 25, and Caroline Pierce, 20, in two separate attacks in Tunbridge Wells, Kent, in 1987, at Maidstone Crown Court on Thursday.
Mr Javid described Mr Fuller’s actions as “horrific” and said an independent inquiry led by Sir Jonathan Michael, a former doctor and hospital chief executive, will examine what happened.
The health secretary said hospitals have been told to improve their mortuary security and the Human Tissue Authority will examine if changes are needed to existing rules around mortuary services.
He added: “My thoughts are with the family and friends of the victims of these horrific acts, as well as all those working in the NHS Trust and wider health service who, like me, will be profoundly shaken by the unspeakable nature of these offences.
“We in government are working closely with the local police force and trust to ensure the families affected get the comprehensive support they need at this time.”
Fuller, now 67, was able to gain access to the mortuary through his role as an electrician in the NHS.
He changed his pleas on Thursday, four days into his trial which heard he had sexually assaulted the two women after killing them.
He had admitted killing the women but originally pleaded not guilty to murder on the grounds of diminished responsibility.
Ahead of his trial, Fuller pleaded guilty to 51 other offences, including 44 charges relating to 78 identified victims in mortuaries where he was working as an electrician.
The victims included three children under the age of 18 and others older than 85 between 2008 and November 2020.
Fuller filmed himself carrying out the attacks at mortuaries inside the now-closed Kent and Sussex Hospital and the Tunbridge Wells Hospital, in Pembury, where he worked in electrical maintenance roles since 1989.
The CPS said police searches of Fuller’s home in Sussex to gather evidence in the murder investigation uncovered four million images of sexual abuse.
While most of these were downloaded from the internet, they revealed Fuller had also recorded himself abusing bodies over the course of his employment at the hospitals.
Having evaded justice for 33 years, he was arrested for murder on 3 December last year following new analysis of decades-old DNA evidence, which linked him to the killings.
Ms Knell was found dead in her apartment in Guildford Road on 23 June, 1987.
Her body showed signs of blunt force trauma to the head, asphyxiation to the neck, and sexual assault after her death, the court heard.
Samples Fuller left on Ms Knell's duvet made Fuller one billion times more likely to be the killer, the CPS said.
Ms Pierce was killed five months later outside her home in Grosvenor Park, on 24 November of the same year.
Neighbours described hearing screams from Ms Pierce’s flat on the night in question before she was then reported missing, and there was no sign of her in her flat.
Her naked body was later discovered in a water-filled dyke at St Mary-in-the-Marsh on 15 December 1987.
Cells on Ms Pierce’s tights made Fuller 160,000 times closer a match for her killer than any other person.
Fuller also kept evidence of himself visiting the Buster Browns restaurant where Ms Pierce worked and photos in SupaSnaps sleeves – the company Ms Knell was employed at when she was killed.
There were reports of “prowler activity” in the lead-up to both women’s deaths, with locals reporting a voyeur looking through their windows.
Images of dead women at the two hospital mortuaries being abused by Fuller were found at his home, where officers also discovered four hard drives with five terabytes of data storage in total attached to the back of a cupboard.
“When these hard drives were examined, they were found to contain a library of unimaginable sexual depravity,” prosecutor Duncan Atkinson QC told the court.
“There were both photographs and videos which showed the defendant sexually abusing female corpses in the mortuaries of the two hospitals at which he worked, first the Kent and Sussex Hospital, where he worked full time from 1989, and then the Tunbridge Wells Hospital, to which he moved in 2010,” he said.
In a police interview, Fuller admitted to using Facebook to search for photos of the people he abused in the mortuary.
In relation to identifying and naming the files containing images of his offending against dead people, he said that he had gone back to name them at a later stage, using the ledgers from the mortuary and identification tags on the bodies, Mr Atkinson QC said.
He added: “He admitted to searching for them on the internet, including on Facebook. He claimed that this would be after the offending, rather than research before offending.”
Mr Atkinson QC said these images provided evidence that Fuller committed the acts out of “sexual gratification” and not mental illness.
“It shows the defendant to derive sexual gratification from sexual activity with those who have died,” he said.
He added: “It therefore provides a reason for the killings, however deviant and repellent, that does not depend on an explanation of mental illness that deprived the defendant of his self-control.”
In a statement, Ms Knell’s family said: “For 34 years we, as a family, the police and press have been focusing on what actually happened to Wendy, wanting to know who did it and how she spent her last moments alive.
“We now know and sadly it is much worse than we could ever have imagined.
“Hopefully, we can now start to grieve and move past the pain, and start to remember her as the beautiful, kind, generous, caring, funny girl she was.
“She had a smile and a kind word for everyone.”
The statement added: “Although the guilty plea won’t change anything deep down as the pain and loss will always be there, it’s good knowing he will not be in a position to hurt or cause any more pain.
“Not just for our family.
“But for Caroline's family and friends who’ve been on this same journey with us over all those years and all the other families this man's affected, we feel deep sadness for all of you.”
The home secretary, Priti Patel, said she hoped the victims’ families can “find some solace in seeing justice finally done”.
Describing the case as “shocking”, she added: “The sickening nature of the crimes committed will understandably cause public revulsion and concern.”
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