The training and advocacy body examined the annual reports and accounts of charitable hospitals, including Nuffield Health and the London Clinic, to assess whether they can successfully demonstrate that they operate for the public benefit.
Sarah Johnston, the report author and a researcher at the DSC, said: "Based on the information supplied in their most recent annual reports and accounts, several major charitable hospitals will struggle to meet the public benefit requirement."
Clinics offered free or subsidised places to people on lower incomes, but it was unclear what percentage of patients fell into those brackets, the DSC said.
Johnston said that fee-charging charities levied high fees that some people could not afford, but Charity Commission guidance says that fees must not exclude people who are poor or unable to pay for the opportunity to benefit from a charity's activities.
The DSC is asking the commission to publish concrete case studies showing how fee-charging hospitals can interpret and act on the guidance.
A spokeswoman for the Charity Commission said the requirement to report on public benefit did not come into force until March, and will apply to accounts due from that date.
"The commission is producing more detailed guidance for fee-charging charities and will include some illustrative examples to assist different types of fee-charging charity, including hospitals," she said.
"Our public benefit assessments and decisions will continue to provide further ilustrative examples, as will charities' public beneift reports."