A jury were told Jack Zarrop, 23, had been let down by police, prison and health staff responsible for his care.
Mr Zarrop died after having been found with ligature in his cell on March 20, 2021.
Dr Anton van Dellen, the senior assistant coroner for west London, has said in a prevention of future deaths report: “In my opinion there is a risk that future deaths could occur unless action is taken.”
There have been 13 self-inflicted deaths at the Category B men’s jail in White City since 2018 - of which Mr Zarrop was the youngest.
He had been arrested by the Metropolitan Police and taken into custody at Heathrow Polar Park station on March 17 of that year.
After being kept overnight, the next day Mr Zarrop appeared before Uxbridge Magistrates’ Court.
A suicide and self-harm warning form was completed, noting that he “would hang himself if he was remanded to prison”.
Despite this, Mr Zarrop was not assessed as being at risk of suicide or self-harm.
The former care-leaver - described at the inquest as “intelligent and charismatic” – had a history of suicide attempts, alcohol and substance misuse and mental health problems.
During a nursing assessment on the morning March 19, Mr Zarrop expressed a wish to see the prison mental health team but was never referred to them.
Asked what mental health meant to him, he replied: “A lot. I have a monologue in my head that tells me I am not good enough and also instructs me to harm myself.”
The inquest scrutinised a process known as Assessment, Care in Custody and Teamwork.
In his report, Dr Van Dellen added: “Training of agency staff in the ACCT process does not appear to be part of the commissioning process by NHS England… This places residents in prison at risk of death given the high level of usage of agency healthcare staff.”
An inquest jury concluded on Friday Mr Zarrop died by suicide.
But along with multiple failures by those responsible for his care, the panel found more should have been done in police custody to support and manage his risks.
Helen Stone, of Hickman and Rose solicitors, representing Mr Zarrop’s family, said: “The jury’s conclusions lay bare how serial and fundamental failures by nearly all those responsible for keeping Jack safe in prison contributed to his death.”
Caroline Finney, of the charity Inquest, added: “Jack’s was one of 13 self-inflicted deaths in Wormwood Scrubs since 2018, a number which reflects that the prison is not a safe or ‘rehabilitative’ environment.
“Jack explicitly asked for support and he was failed.”
A Prison Service spokesman said: “We want to see far fewer self-inflicted deaths and self-harm in custody which is why we have increased staff training on self-harm prevention, are working with the NHS to improve mental healthcare and fund the Samaritans.
“In his most recent inspection, the Chief Inspector of Prisons found vulnerable prisoners at HMP Wormwood Scrubs are safe and treated with respect on arrival.”
She added there is nothing to suggest a sudden or unusual rise in the number of self-inflicted deaths at Wormwood Scrubs.
The number has been consistently no more than three a year between 1997 and 2022, with the exception of 2013 when there were five.