Members of the London Assembly Police and Crime Committee expressed concern about the lack of detail around Khan’s plans for a so-called Violence Reduction Unit (VRU).
The scheme aims to use the public health approach to crime, successfully used in Scotland, where police, housing, health and care workers join together.
But in a letter to the mayor, committee members said: “We are concerned that the narrative around the VRU may give some Londoners the impression that it is set up and taking action, when in fact it is very much in the early stages of development.”
They claim the VRU’s funding from surplus business rates is “far from sufficient to resource the unit over the long term”, and called for a move away from the focus on young people, knife crime and gangs.
Members want the unit to tackle a broad range of violence and the particular issue of adverse childhood experiences.
There is evidence that exposure to domestic violence as a child and being excluded from school can in the worst cases lead teenagers to kill.
Committee chairman Steve O’Connell said: “Londoners are heartbroken to hear about the near-daily carnage on our streets, the young lives lost and the misery for families and communities.
“The mayor’s new Violence Reduction Unit will need to demonstrate that it brings something different to the table. It cannot simply be a rebranding exercise of existing programmes and policies.
“We cannot emphasise enough how critical it is that the unit tackles the traumatic situations that children might live through in order to break the cycle of violence.
“We do not underestimate the challenge ahead but it’s time for the mayor to take even further and drastic action because London is crying out for change.”
In a letter to Khan, committee members called for the VRU to tackle all kinds of violence including domestic; focus on prevention and school exclusions; regulate social media platforms; and adopt a Prevent-style approach used to counter terrorist activity.
There have been 125 homicides in London so far this year, the highest number this decade.
A spokesman for the Mayor of London said: “The number of violent deaths both in London and across the country is tragic. Violent crime in our city leaves families broken and communities devastated.
“The causes of violent crime are extremely complex and are decades in the making, made worse by years of austerity and governments cuts to the police and youth services.
“The Mayor is expanding City Hall’s long-term public health approach to tackling the root causes of all forms of violence by setting up a Violence Reduction Unit in London.”
The spokesman said Khan was “leading from the front” by working in partnership with police, the health service, local authorities, community groups and youth services.
“It is clear there is no one single solution to tackling this complex issue,” they added.
“We are working hard to challenge the perception it is safe to carry a knife and the VRU will seek to better understand where to make positive early interventions, because we know some offenders have themselves been victims or witnesses of violent crime in childhood.
“This will work alongside (our) work to deliver the Mayor’s comprehensive strategy to tackle violence against women and girls in all its forms. However, the Mayor is clear that tackling the causes of violence will not happen overnight.
“We need the London Assembly and others to join us in putting pressure on ministers to reverse their £1bn of damaging cuts to the police and youth services.”