A life-long injunction made in 2001 has allowed Venables to live under a cloak of anonymity since his release from a life sentence for the kidnap, torture and murder of the two-year-old in February 1993.
Lawyers for Ralph and Jimmy Bulger said certain details about the killer, including identities given to him up to 2017, were “common knowledge” and easily accessible online.
They asked the president of the Family Division, Sir Andrew McFarlane, to vary the order so it would no longer protect this information.
In a ruling yesterday, the judge refused to alter the anonymity order, which he said was to protect the “uniquely notorious” Venables from “being put to death”.
He said: “There is a strong possibility, if not a probability, that if his identity were known he would be pursued, resulting in grave and possibly fatal consequences.
“This is, therefore, a wholly exceptional case and the evidence in 2019 is more than sufficient to sustain the conclusion that there continues to be a real risk of very substantial harm to [Venables].”
The judge added: “My decision is in no way a reflection on the applicants themselves, for whom there is a profoundest sympathy.
“The reality is that the case for varying the injunction has simply not been made.”
Anyone who breaches the wide-ranging injunction faces prosecution for contempt of court.
Speaking outside court after the ruling, solicitor advocate Robin Makin, for the Bulgers, said: “The authorities seem to be hell-bent on protecting JV regardless of the risk to others and this has been a primary driving force behind Ralph and Jimmy’s application.”
Sir Andrew refused permission to appeal against the ruling but Mr Makin said the Bulgers may consider pursuing a challenge at the Court of Appeal.
James Bulger was killed by Venables and Robert Thompson, who were both aged ten, after they snatched him from a shopping centre in Bootle, Merseyside.
In his opening remarks, the judge said the crime had “profoundly shocked the nation”, adding: “The family of young James Bulger were and are deserving of the greatest sympathy as the indirect victims of this most horrific crime.”
Venables and Thompson were both granted life-long anonymity by a High Court judge and have lived under new identities since their release from custody.
The court order was amended in relation to Venables after he was convicted of further offences in 2010 and February last year.
He was jailed for three years and four months last year after admitting surfing the dark web for extreme child abuse images and possessing a “sickening” paedophile manual.
Police found more than 1,000 indecent images on his computer. It was the second time he had been caught with such images.