The Challenge has brought the legal action after its contract to deliver the government-backed programme for 16- and 17-year olds in London, the South East and the West Midlands was not renewed earlier this year.
The charity, which had been locked in a disagreement with the NCS Trust over a shared IT system, said it had witnessed the programme being "profoundly mismanaged" by the trust.
It said it wrote to the Department for Digital Culture, Media and Sport (DCMS) in July outlining its concerns.
In a statement, the charity's chief executive Oliver Lee said: "On 31 July, our awards for future contracts were withdrawn.
"We confirm that The Challenge has also brought a legal action against NCS Trust, the details of which are now a matter of public record."
The trust's customer relationships management IT system is believed to be at the centre of the dispute, with The Challenge claiming technical problems prevented thousands of young people from completing the first day of the programme.
The document, lodged in the High Court, alleges this cost the charity £12m in lost earnings and additional expenditure.
It has also raised concerns about potential safety risks from the NCS using a "flawed medical assessment process", which it claims fails to record whether young people on placements have medical issues such as potentially fatal allergies.
The charity also faces staff redundancies and having to cut the number of placements it runs after NCS said its contract would not be renewed from 2020.
The Challenge confirmed to CYP Now that the total sum in the legal action is £22m.
Michael Lynas, chief executive officer of NCS Trust, said it had been unable to reach an agreement with The Challenge over a contractual requirement to use a shared IT system.
"The Challenge is very unhappy about this decision and, since then, it has made what we consider to be false allegations about NCS Trust before launching legal proceedings.
"There are no failures with the trust's centralised customer relationship (CRM) system. In fact our largest new partner was fully set up and running, and able to undertake all aspects of the work required by them on the trust's system, within three months.
"We reject all the allegations made by The Challenge and will be mounting a robust defence."
Lynas said the trust "cared passionately" about the safety of young people and its partners had "rigorous contractual obligations" in place to ensure safety standards, which were independently audited.
"When any risks are raised, we take immediate action. We have put extra independent assurance in place for The Challenge this year and no evidence of additional risk was identified. This assessment was confirmed by The Challenge," he said.
