Sixty-two per cent of people think that those caught carrying a knife in public should automatically go to jail, a poll conducted for the BBC suggests.
A compulsory jail term was backed by 57% of 305 16 to 24-year-olds polled by the BBC's Panorama programme. More than 1,300 people were questioned in total.
The maximum sentence for knife carrying was doubled in 2007 to four years - this is rarely handed down, however.
But young offenders in jail for knife attacks said this should be mandatory.
The poll was carried out as part of research into Jailed for a Knife, a Panorama programme examining the causes of Britain's knife culture and how best to tackle it by speaking to those responsible - youngsters convicted of carrying, using, and even killing with a knife.
Given rare access to the prisoners in their cells, Panorama interviewed five inmates in two young offenders institutions, three of whom had killed other young people with a knife and two of whom had committed grievous bodily harm (GBH).
Young people campaigning against knife crime give their view of the poll results
Thirty four teenagers died as a result of knife attacks in the UK last year.
And over the last decade there has been a significant increase in the number of people sentenced for carrying a knife.
In 1996, 890 people were sentenced for possession of a knife in a public place. In 2006 the total was 6,284.
In the same period the number of those under the age of 18 sentenced went from 114 in 1996 to 1,226 in 2006.
Amid growing public concern, the government took the step in February 2007 of increasing the maximum sentence for carrying a knife from two years to four.
And in June 2008 it introduced new measures under which anyone over the age of 16 found carrying a knife in public should expect to be prosecuted.
However, the poll for Panorama suggests the majority of people think the law still does not go far enough.
Sixty-one per cent of those questioned disagreed when asked if the current law is enough to stop under 16s carrying a knife. In the 16-24 age bracket 59% disagreed.
Forty-three per cent of people polled for Panorama said that under 16s should automatically go to jail for their first offence. A similar proportion, 42%, of 16-24 year-olds questioned agreed.
The five young offenders whom Panorama interviewed in Jailed for a Knife told the programme that prior to being incarcerated they had not taken the threat of prosecution seriously.
"Never thought about it, you know, that's being truthful, I never even thought about that," one said. "Everyone thinks 'oh yeah, I can do this and I'll get away with it, it's gonna be nothing'."
The young offenders said that the best deterrent would be for custodial sentences to be automatic, and for the maximum penalty of four years to be rigorously applied.
"I've seen people come in and out of here three or four times since I've been in jail for a knife or GBH - 18 months," one offender said.
"To be honest I agree with the people when I read the papers that sentences should be longer - it should be a sentence that's going to get through to them, not this in and out of jail business," he added.
However, a four-year sentence is only given in exceptional circumstances - in fact in 2007, the year the measure was introduced, only one person was given a sentence, for possession of an offensive weapon, which amounted to at least four years.
How to prevent youngsters from carrying a knife in the first place has been the subject of a charged national debate.
The inmates Panorama spoke to said communicating more effectively with youngsters is an essential component.
Many of them said it was only the harsh reality of prison life which had forced them to consider the full consequences of their actions and there was a call for more youngsters to hear about such experiences first-hand before they too ended up in jail.
This view was supported by the vast majority of those who took part in Panorama's poll.
Eight four per cent of people questioned said more young people should hear first-hand experiences of knife crime from reformed young offenders - support for such a measure rose to 90% among 16-24 year olds.
Panorama: Jailed for a Knife on BBC One, Monday, 12 January, 2009 at 8.30pm.