More than half the prisoners in England and Wales who kill themselves are on remand, a prison reform charity says.
The Howard League said local prisons were often overcrowded
The Howard League for Penal Reform says remand prisoners make up only a fifth of the prison population.
It said that remand prisoners are often held in "overcrowded and overstretched local prisons".
The prison population stood at 76,266 on 1 July, according to the Prison Service. It has a self-harm policy to offer help to those at risk.
Of the 804 suicides between 1995 and 2004 inclusive, 65 were female and 739 were male, the Howard League said in its report, published on Tuesday.
The vast majority (92%) hanged themselves.
Other findings from the Howard League included that local prisons had the highest rate of suicide.
The 15 prisons most affected by suicides had on average 21 suicides, with the highest being 27 suicides.
Seventeen children killed themselves in prison, the Howard League said.
Pauline Campbell's 18 year-old daughter Sarah died after taking an overdose of anti-depressant drugs in Styal Prison, Cheshire.
She told BBC Five Live's Breakfast programme that the problem of prison suicide was an affront to a society that seeks to be a civilised democracy.
"Anyone who's convicted of a criminal offence clearly must be dealt with before the courts.
"If it involves a prison sentence, I would add that all prisoners are owed a legal duty of care by Her Majesty's Prison Service".
She added that "the present shocking death toll whereby two people a week take their own lives in prisons in England and Wales - it's frankly an affront to a society that seeks to be a civilised democracy.
Help for prisoners
"The shocking death toll is causing widespread concern and frankly a loss of public confidence in the criminal justice system," she added.
Home Office minister Baroness Scotland said one of the key priorities for the Prison Service was to reduce the amount of self-harm by prisoners.
"Every year thousands of offenders pass through the prison system, and in the last ten years we have been responsible for more than 1.5 million prisoners.
"At any one time, this population contains a high proportion of very vulnerable individuals, many of whom have experienced negative life events and are at serious risk of self harm and suicide".
She highlighted the fact that "in any given month, prison staff successfully care for approximately 1,500 prisoners assessed to be at particular risk".