The Fishmongers' Hall attacker's local Prevent team had "no specific training" in handling terrorist offenders, a court has heard.
Convicted terrorist Usman Khan, 28, killed Cambridge University graduates Saskia Jones, 23, and Jack Merritt, 25, during a prisoner rehabilitation event near London Bridge on November 29 last year.
Khan, who was armed with two knives and wore a fake suicide vest, was tackled by members of the public with a narwhal tusk, a decorative pike and fire extinguisher.
The attacker, who had been living in Stafford, was then shot dead by police on London Bridge.
A full inquest, due to start at the Old Bailey on April 12 next year, will examine how the tragedy happened and if it could have been stopped.
At a pre-inquest hearing on Friday, a lawyer for Mr Merritt's family suggested there was already evidence of a "systemic problem".
In this case already on the material that has been produced, we have all the Prevent officers from Staffordshire saying they had no specific training in handling terrorist offenders.
Henry Pitchers QC, for Ms Jones's family, said the question was not whether Prevent or probation knew there was a risk but whether they "should have had an inkling".
Mr Pitchers pointed out that Khan had been assessed as the "highest level of risk" and had 22 licence conditions on his release.
He said police officers made their last unannounced visit on November 14 2019, just over two weeks before the attack.
They found his flat to be dark, Khan was not happy about photos being taken of his Xbox games and wanted to speak to his solicitor, Mr Pitchers said.
Khan was unemployed, lived alone and his mentoring had ceased, which was "hardly a reassuring profile", the lawyer added.
Mr Pitchers went on to question security around the Learning Together event at Fishmongers' Hall.
We know from the evidence his attendance to this event was expressly authorised. It was not slipping between the conditions.
He said those who gave permission did nothing to notify Scotland Yard, City of London Police, the Fishmongers' Company or the organisers of the Learning Together event.
There was no security check on the door, not even a rudimentary bag check.
During the hearing, the victims' family lawyers also resisted any attempt for their inquests to be heard together with Khan's.
Mr Pitchers said it would be a "source of real, significant and persistent distress throughout the course of the inquest" if the coroner agreed to requests for involvement on behalf of Khan's mother Parveen Begum.
Earlier, Mrs Begum's lawyer Jude Bunting had abandoned an attempt to have the inquests joined but asked that she be given "interested party" status in the victims' inquest.
Mrs Begum was deeply shocked by the events of November 29. It was a tragedy Jack Merritt and Saskia Jones were killed. As a mother herself, Mrs Begum still finds it hard to believe such terrible damage could be caused by her son.
She offered her sympathies to the families of the victims, he said.
Mr Bunting said the family were "not aware of Usman Khan's mindset or intentions". He said the family wanted to understand how it happened and ensure "lessons are learned" so no-one has to go through the anguish that the victims' loved ones had suffered.
Chief Coroner Mark Lucraft QC is expected to rule on the issue later.