Six youngsters who experienced first-hand the trauma caused by violence with the weapons have demanded a meeting with him after compiling an action plan of how to prevent more young lives being lost.
Delivering a letter to Downing Street on Thursday, which was signed by more than 100 young people, they also presented the 12-point manifesto on what they think would make the streets safer.
The news comes after official figures showed knife crime in England and Wales hit a record high in 2018/19, up 8% on the previous year.
In the letter, the youngsters said: “More and more of our generation are still dying.
“More needs to be done, as soon as possible.
“As Prime Minister we need you to make this problem your top priority.”
They worked with the All-Party Parliamentary Group on Knife Crime, as well as youth charities Barnardo’s and Redthread, on a report entitled There is No Protection on the Streets, None, as part of their campaign.
The manifesto includes calls to tackle what the group believe are underlying causes of violent crime, such as lack of housing, youth services and jobs, as well as a bid for more community police officers to build relationships in neighbourhoods.
Barnardo’s chief executive Javed Khan said: "As leaders in Government, parliament and charities, we must come together to help them by addressing the poverty of hope felt by many children and young people across the country, who see little or no chance of a positive future.
"This starts with the new PM listening to their concerns and agreeing to meet them. They are the people most affected by the violence and their voices need to be heard."
It comes as a police officer in London is critical condition after being stabbed a number of times in the head and body with a machete.
Following the attack, the PM visited Leyton and promised offered his "sympathies" to the injured police officer.
He said: "What this underscores for me is the bravery of our police, people who actually go towards danger to keep us safer."
Mr Johnson added: "Also what it shows to me is the vital importance of investing in policing, that's why we're putting another 20,000 officers out on the street, and giving officers the legal powers and support that they need to tackle knife crime and other violent crime."
Campaigner Zak Hall, from Redbridge in east London, told PA urgent action was needed to tackle the “vile culture” of knife crime that is “creeping in”.
The 24-year-old told how both his brothers were victims of knife crime and one of his friends was murdered last year.
He thinks those aged 14 to 21 are in the greatest danger of being drawn into knife crime and at risk of being victims.
Mr Hall said: “Some just feel it’s the new reality.
“But it needs to stop, it’s so dangerous. It’s really scary, it’s horrible.”
Labour MP Sarah Jones, chairman of the parliamentary group, said: “Our new Prime Minister must take responsibility for solving the epidemic of serious violence facing our country.
“He needs to be clear this will be both a national and personal priority.
“The response to this emergency must be led from the very top, and the voice of young people must be at the forefront.
“Boris Johnson has suggested that knife crime can be solved simply by increasing stop and search, but the solutions proposed by young people today show he needs to think much bigger. I hope he listens and agrees to meet them in person.”
Last week, MPs branded youth violence a “national emergency” and called the Government’s response to date “completely inadequate”.
Police recorded more than 43,000 incidents involving knives or sharp objects in the year to March, according to figures published by the Office for National Statistics in July.
A Home Office said it is investing more than £220 million in projects that “steer young people away from crime”.
A department spokesman said: “This Government will not stand by while more young lives are lost – we are determined to crack down on the scourge of knife crime.”