Durham Police confirmed 1,085 men had made reports of abuse at the centre in Medomsley.
The force said it was trying to contact and question former centre staff.
Inquiries were prompted by the jailing of two ex-staff members, who have both since died, in 2003 and 2005.
Solicitor Alistair Smith, who is representing 90 victims, urged the government to speed up compensation payment to victims.
Mr Smith said: "I've had men in tears in their 50s and 60s - there is a lot of hurt there and they've kept this to themselves for 30 and 40 years.
"These are victims and they deserve having the government deals with this now. They should not have to wait and go through the civil process for compensation - that takes too long."
But, the Ministry of Justice said the police probe was slowing down progress.
A spokesman said: "We are not delaying the release of compensation to victims of Medomsley Detention Centre and we are doing everything we can to progress claims as quickly as possible.
"However, many cases are still subject to an on-going police investigation for which we are co-operating fully and providing historical records."
The investigation was triggered after former prison officer Neville Husband was jailed for eight years in 2003 for abusing five youths.
The publicity surrounding the trial led to others coming forward and he was subsequently jailed for a further two years for other attacks.
He died in 2010, after being released from prison.
His former colleague Leslie Johnson, who was jailed for six years in 2005 for sexual offences, has also since died.
Durham Police said: "We are currently in the process of tracing and speaking to a number of former prison officers who worked there during the years in question."