Footage recorded by Streets Kitchen, which supports those sleeping on the streets, showed some being thrown into the back of a bin lorry.
Deputy leader Adam Harrison said initial investigations found “there was operational involvement from Camden”.
The tents were cleared from the area after the Metropolitan Police issued a S35 dispersal order, which requires people to vacate an area for a maximum of 48 hours.
The force said it worked with UCLH and other partners in response to concerns for patient welfare near the entrance on Huntley Street.
Police received reports of “drug dealing, urination and staff being intimated or verbally abused by some of those begging and sleeping rough”.
Following an “urgent investigation”, Mr Harrison said on Wednesday: “It’s important to acknowledge what happened on Friday was unacceptable... it is clear that something has gone wrong here.
“Whilst this dispersal order was applied for by University College Hospital London and enforced by the police, we acknowledge that waste collection services were arranged through the council and our rough sleeping support services were engaged to support people affected.”
A spokesperson for refuse firm Veolia said it acted “on behalf of and under the strict supervision of Camden Council, and the police when needed”.
They said: “We follow all the procedures and requirements needed when it comes to removing sensitive items.
“We are working internally and with Camden Council to review how requests of this nature will be handled in the future.”
A UCLH spokesman previously said the action was taken due to “public health concerns” outside Grafton Way Building, which houses units treating immunocompromised patients.
They added: “UCLH is deeply committed to improving the health and wellbeing of homeless people and we provide a number of services for this vulnerable group.”
But Streets Kitchen founder Jon Glackin rejected accusations the homeless men were dirty.
He said he wanted to see a constructive community response following the removal of the tents and added that the organisation was co-hosting a public meeting on Thursday at St Michael’s Church on Camden Road.
One homeless man, who claimed he has received no warning of the raid, told them: “My clothing, everything from the past 23 years, all my belongings, is away... is gone.
“The tent was like my home. It was where I found peace. I feel devastated you know.”
Mr Harrison said the incident did not reflect the council’s values, adding: “We will make sure this is clear and understood at every level of the organisation.
“We are determined to make improvements to how rough sleepers are supported in the borough.”