Onlookers clapped and some motorists beeped their horns in a show of support.
Addressing the gathering in Hyde Park Mr Brown said stronger penalties sent "a clear message to every young person carrying a knife that there will be no excuses and no exceptions".
He added that people need to make sure "every young person has something to do with their time and isn't just hanging around."
"The country is listening to you," he added.
Speaking to the crowd Metropolitan Police Commander Mark Simmons said: "We have arrested over 3,000 people and every person we arrest we are prosecuting and we are putting them in front of the courts.
"We want to work with your communities and we will be absolutely relentless in our pursuit of people that use knives."
'Shame on you'
Police Minister Tony McNulty also spoke to the crowd and said: "We shouldn't have to come here to celebrate lives that have been cut short.
"If you know someone who carries a knife, shame on them, if you know and don't do anything about it, shame on you.
"If your local community isn't doing enough, speak to your local councillor and if they don't do enough sack them at the next election or get hold of your MP and if they don't do anything sack them."
Gary Trowsdale, special projects organiser for the Damilola Taylor Trust - which organised the event, said: "It's more about the people who have decided enough is enough, and before it happens to someone in their family, they want to come together and make a stand."
The idea for the peace march was started on Facebook
The idea for the People's March was started on Facebook by Sharon Singh and Gemma Olway, both 26 and living in south-west London. It received the backing of several national newspapers.
Murdered schoolboy Damilola Taylor's father Richard said: "There are other ways by which you can sort out a fight rather than use a knife. We have had enough of this."
Mr Taylor also called for families to take greater responsibility for "guiding" their children.
Barry Mizen, father of 16-year-old Jimmy, stabbed this May, said: "I am more than glad to be here today if it helps make a difference and in memory of our son.
"If we do nothing it will just get worse. I can't see this changing at all if we bury our heads in the sand."
Rosie Ogazi, whose 21-year-old brother Antony was murdered in Stockwell in May, said: "Since my brother died I'd felt I had not been doing anything but now I feel like I'm doing something constructive."
Among the marchers were former EastEnders actress Brooke Kinsella, whose 16-year brother Ben was stabbed to death in June, and Caroline Kingonzila, mother of promising footballer Oliver who was killed last Saturday.
Hundreds of people participated in another anti-gun and knife crime march - Not Another Drop - from Harlesden to Wembley Stadium, north-west London.
Hundreds also attended an anti-knife march in Inverclyde, Scotland.
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