The march from Camberwell, south London, to Downing Street has been called to raise awareness of vulnerable people who used the service.
The charity was closed following a row over funding. Kids Company has denied allegations of financial mismanagement.
The prime minister said the government had been right to give the charity one more chance.
Before it shut its doors on Wednesday, Kids Company provided practical, emotional and educational support to some of the most deprived and vulnerable inner-city children and young people in London, Liverpool and Bristol. It was founded in 1996 by Camila Batmanghelidjh.
David Cameron said he was sad at the closure of the charity, which had been given a Â£3m government grant last week.
He said: "The government thought it was the right thing to do to give this charity one last chance of restructuring to try and make sure it could continue its excellent work.
"Sadly that didn't happen, not least because of the allegations that were made and private donors withdrawing their money but I think the government was right to say let's have one last go trying to keep this charity going, given the work it's done for so many young people."
Some 150 people gathered outside the charity's former centre in Camberwell to take part in the march to Parliament.
Lisa Moodie, who has been a youth worker with the charity for seven years, said: "Today isn't about Camila, it's about love, it's about making sure the children's voices are heard.
"I agree people need to be accountable for what happens to our young people, it's not acceptable that we just leave them discarded. These are very vulnerable young people, they live chaotic lifestyles.
"When they mess up, we're here for them just as your parents would be. It's very difficult to measure success in a hospital - it would be how many broken bones do you have. How we measure success can be in small things. It might be learning how to use a knife and fork."
Anita Ebirim, who brought her eight-year-old daughter to the charity, said: "Why did they close Kids Company? It's a place we come to save our lives.
"Every day we come here to eat our lunch... we get breakfast, we get clothes.  A lot of young men come who don't work, but it stops them messing around and getting into drugs."
Kids Company employs 600 paid staff, as well as working with a pool of about 8,000 volunteers and 500 students.
Marie, a 30-year-old volunteer from Wimbledon, said: "It makes no sense, it hasn't really sunk in yet. The kids keep coming and find out by the notice on the gates . We didn't have time to say our goodbyes to the kids."
The charity has been beset by problems, including allegations of financial mismanagement and accusations by former staff that the charity failed to deal with allegations of serious incidents.
Kids Company is also being investigated by the Met Police's Sexual Offences, Exploitation and Child Abuse Command.
Ms Batmanghelidjh has strongly denied any wrongdoing.
Supporters of the closed charity Kids Company are taking part in a march in London.