Wormwood Scrubs prison in west London has been plagued by allegations of brutality
Twenty detectives have been assigned to the Scotland Yard investigation which has become the biggest police inquiry into alleged prison brutality.
Some of the accusers allege they were racially abused during assaults.
Daniel Machover, the solicitor who made the original allegations involving eight prisoners, has now passed the details of 25 other inmates to the Metropolitan Police.
He said: "They seem to be taking it seriously."
'Serious questions'
Nine staff at the jail were suspended two weeks ago after an internal Prison Service inquiry into the claims found "serious questions" needed to be answered.
A Scotland Yard spokesman said: "Police have now got the names of more than 30 people who could have information."
He said these included potential witnesses as well as alleged victims.
Mick Flynn, deputy director of the Prison Reform Trust, said: "The weight of information which has been amassed by the solicitors is unique.
"Each case details systematic brutality and physical and verbal abuse.
"Internally the prison has been unable to deal with the matter and it took a solicitor outside the jail to raise it, which raises questions about the internal monitoring and complaints procedure at Wormwood Scrubs."
Mr Flynn said the allegations and the way they were dealt with suggested there was a "culture of turning a blind eye" at the prison.
A Prison Officers Association spokesman said prisoners were "jumping on the bandwagon" by adding their voices to the original allegations.
He said: "What happens in a lot of these cases is inmates are restrained using Home Office approved "control and restraint" techniques but bang their heads or whatever accidentally."
It is rare for prison officers to be convicted of assaulting inmates but in the late 1970s eight staff at Hull jail were found guilty of conspiring to assault prisoners and were sacked.