But now anyone over 16 can expect to be prosecuted on their first offence.
Mr Brown met representatives from the Association of Chief Police Officers (Acpo) and the director of public prosecutions at the Downing Street meeting.
Also present were Home Secretary Jacqui Smith, Justice Secretary Jack Straw and Attorney-General Baroness Scotland.
Mr Brown said: "We want people to understand, particularly parents, that when children and young people are carrying knives, they are putting other children and young people at risk."
The director of public prosecutions, Sir Ken Macdonald QC, told Mr Brown at the meeting: "When people come to us their expectation is a prosecution will follow.
"What we are proposing is that if people are carrying a knife and are prosecuted for other offences, they will be prosecuted for the knife too.
"We have set out some further guidance that the public interest is in favour of prosecution.
"It has become fashionable [to carry a knife]. What we want people to understand is they put themselves at risk carrying these sorts of weapons."
Acpo president Ken Jones said officers would still use discretion.
He said: "But the point at which they now would consider this individual has no previous conviction, there are no aggravating factors, that he or she might be subject to a caution, we are now saying no, that is now removed.
"We are not out to criminalise people who have a good reason for being in possession of a knife, but frankly what good reasons would a youngster have for even carrying a penknife?"
But Professor Rod Morgan, former chairman of the youth justice board and one of the government's advisers on youth justice, branded the latest idea "gesture politics".
He said: "The police have all the powers they need to deal with what is a problem in some areas, but they need to be given discretion to respond to events as they find them."
And Detective Chief Superintendent John Carnochan, head of the violence reduction unit in Glasgow, said criminal justice did not work on its own.
"We need to do other things - if we want to change attitudes, if we want to change culture, that's not a role simply for the police. That involves everyone," he said.
The change in policy on cautions is part of a package of measures announced by the Home Office.
Gordon Brown on knife crime
Police in areas suffering from knife crime will receive Ł5 million to help fund greater use of searches, courses for young people caught with knives and home visits and letters to parents.
A new scheme in which hospital A&E units in "hotspot" areas would pass information about injuries caused by weapons to the police is also being discussed.
Metropolitan Police figures show that the number of victims of knife crime have been going down.
In the year to March 2008, there were 10,220 such crimes, compared with 12,124 for the previous year - a reduction of 15.7%.
But the number of 11 to 18-year-olds attacked with knives between April and July 2006 rose by 4.5% compared with the same period in 2005.
Last year 27 teenagers in London met violent deaths, compared with 17 in 2006 and 15 in 2005.
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