It comes as the charity’s flamboyant founder Camila Batmanghelidjh lashed out at ministers, civil servants and the media, claiming the organisation was the victim of a “trial by media”.
Up to 36,000 vulnerable children and young people are said to have received support from Kids Company, and there are fears many could slip through the net unless immediate plans are put in place to continue services.
Richard Curtis, founder of The Root Of It, an organisation which works to raise standards in special needs services in schools, said he is attending the emergency meeting “to discuss what the next steps are”.
He said: “It’s about putting in services that are going to help these children so they are not abandoned.
“If there is not something put in place very quickly it’s very likely that things will start to deteriorate in those areas with those families that Kids Company has been supporting.”
The meeting follows emotionally charged scenes yesterday outside the Kids Company centre in Peckham, south London, where the charity was founded 19 years ago.
Children and parents waving placards protested against the closure while staff left the centre in tears, exchanging hugs with families they had worked with.
Ms Batmanghelidjh claimed one child was so upset she had to talk him out of jumping off a platform in front of a train in a phone call.
The charity worked with children in London, Bristol and Liverpool, and councils, the Government and charities have all said the welfare of the children is their top priority.
Mr Curtis said an inquiry should be set up to uncover why the charity collapsed so suddenly, but said in the meantime the Government and organisations need to step in “to fill that void”.
He said: “I do believe there should be an inquiry into how it got into this mess, but my best hope for this afternoon would be that a plan is identified and at least the first few steps are agreed.
“The scenes we saw yesterday outside the Kids Company very much reflect how the families feel abandoned at this moment in time.
“What’s important now is being able to provide and reassure them that something is being put in place so things don’t spiral out of control, because a lot of the emotions come out of fear of the unknown about what is going to happen to them.
“So many of them have depended on the support of Kids Company.”
Ms Batmanghelidjh repeated her belief that claims of financial mismanagement at the charity were unfounded and condemned David Cameron’s administration for cutting off funds.
She told the BBC Radio 4 Today programme: “If we were so dysfunctional, why did the Government hand over £7 million worth of taxpayers’ money?”
Ms Batmanghelidjh said former Tory minister Tim Loughton was “disingenuous” in claiming there were no measurable results for Kids Company’s work.
She said: “The problem with this situation is we are not dealing with facts. It’s all rumours and conjectures. If anyone sat with me and actually looked at the facts, the facts with evidence, it would be very different.”
She continued: “It’s trial by media. It’s not everyone is out to get us, we have become a football for the media and the civil servants over the summer. It’s so destructive to these children.”
The charity had a string of celebrity backers including rock band Coldplay and artist Damien Hirst, and was lauded by Mr Cameron as the embodiment of the Big Society.
But ministers and civil servants said its sudden collapse this week followed years of questions being raised over its financial management.
According to reports, Michael Gove said Government funding for the charity should be stopped while he was education secretary, but he was overruled by Mr Cameron.
It has emerged the charity shut its doors yesterday after a donor pulled out of giving £3 million when they learned of allegations of abuse and sexual offences related to the charity.
Ms Batmanghelidjh said she had “honestly no idea” if the Prime Minister personally intervened to keep public money flowing to Kids Company three years ago.
She warned that Kids Company had been left “carrying a statutory caseload of very disturbed children and young people who are self-referring off the street” but should have been provided for by the Government.
She said: “I wanted Government to come and take responsibility for child protection and child mental health cases that a charity like ours shouldn’t be holding.”
The Charity Commission, which regulates charities in England and Wales, said it “acted quickly” when recent claims of bad financial management came to light.
It said it met trustees of the charity on July 9 about funding and proposed governance changes.
A week later officials spoke to former employees to discuss allegations of inappropriate spending and breaches of financial controls, and to discuss concerns about the charity’s viability.
At a meeting with the charity on July 21 it was agreed Kids Company would launch an independent probe into the allegations. The charity was in the midst of shake-up in the way it was run when it shut down.
The Charity Commission said: “The priority for the trustees during closure is the welfare of the charity’s vulnerable beneficiaries.
“We have received assurances from the charity that, working with government agencies and charities, steps have been taken to ensure the transfer of the care of the beneficiaries and there will be clear sign-posting so that they know where to go for alternative help.”