More than 200 people have died of "non-natural" causes in detention since 2014, the Equality and Human Rights Commission said.
Most happened in prison, where official figures show there were 178 self-inflicted deaths and 11 apparent homicides in the two years to December.
The Commission acknowledged that improvements had been made in police custody, psychiatric facilities and jails but said it was "not enough".
Professor Swaran Singh, EHRC Commissioner on adult deaths in detention, said: "Failure to make progress in reducing the number of avoidable deaths is a national stain that we should no longer tolerate in modern civilised society.
"Progress has been so slow that we have continued to see a large number of tragic cases in the past two years where that responsibility has not been met.
"There is a corrosive culture of secrecy and blame which is holding back the progress that's so desperately needed.
"It is tragic that we appear to be going backwards not forwards in some areas, whilst avoidable deaths continue to rise."
The Commission said there has been a reduction in the use of police cells as places of safety for people detained under the Mental Health Act, and a fall in deaths of detained patients in psychiatric hospitals.
Its report added that some changes have been put in place or are in progress to address problems with assessing risk and offering better support for prisoners with mental health conditions.
The EHRC called for a change in the law to ensure psychiatric hospitals, prisons and police forces publish action plans to address recommendations from investigations and inspections
Figures for 2014/15 showed there were 17 deaths "in or following" police custody in 2014/15, including eight people who were identified as having mental health concerns.
A Prison Service spokesman said: "We take our duty of care to prisoners extremely seriously. Staff provide support to prisoners at risk of self-harm and suicide every day and the EHRC has recognised the work that we are doing in this important area.
"We will continue to improve our safer custody support and are working with the Department of Health to reform mental health services in the criminal justice system.
"As the Prime Minister announced recently, we are taking steps towards full co-commissioning for governors and NHS England – meaning prison leaders can have much more say in defining the kind of services their prisoners need and how the available budget is used.
"We are investing £1.3 billion to transform the prison estate over the next five years, to better support rehabilitation and tackle bullying, violence and drugs."