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The Howard League for Penal Reform has been notified of 102 people dying by suicide behind bars since the beginning of 2016 - one every three days.
At Peterborough and Whitemoor Prisons, the total for 2013-16 was eight deaths.
None were recorded over this period at Littlehey Prison near Huntingdon.
With five weeks remaining until the end of the year, it is already the highest death toll in a calendar year since current recording practices began in 1978. The previous high was in 2004, when 96 deaths by suicide were recorded.
The report states that urgent action is needed, and that prisons must become safer, healthier places to reduce suicide risk.
The report finds that the rise in the number of prison suicides has coincided with cuts to staffing and budgets and a rise in the number of people in prison, resulting in overcrowding. Violence has increased and safety has deteriorated.
Prisoners are spending up to 23 hours a day locked in their cells, the imposition of prison punishments has increased, and a more punitive daily regime was introduced in prisons at the same time as the number of deaths by suicide began to rise.
The prison suicide rate, at 120 deaths per 100,000 people, is about 10 times higher than the rate in the general population.
The report states that investing in staffing must go hand in hand with a reduction in the prison population if prisons are to be made safer.
Frances Crook, Chief Executive of the Howard League for Penal Reform, said: "The number of people dying by suicide in prison has reached epidemic proportions. No one should be so desperate while in the care of the state that they take their own life, and yet every three days a family is told that a loved one has died behind bars.
"Cutting staff and prison budgets while allowing the number of people behind bars to grow unchecked has created a toxic mix of violence, death and human misery.
"This report makes clear that there are practical steps that can be taken to make prisons safer. I am due to meet the Secretary of State for Justice today (Monday 28 November), and I shall be outlining the Howard League's plan to reduce pressure on the prison system.
"By taking bold but sensible action to reduce the number of people in prison, we can save lives and prevent more people being swept away into deeper currents of crime and despair."
Andy Bell, Deputy Chief Executive of Centre for Mental Health, said: "Every loss of life through suicide is a tragedy for everyone involved.
"Prisoners face a very high risk of suicide and it is essential that prisons and health services work together to prevent loss of life. This requires a fundamental change to the way prisons work, creating an environment that supports wellbeing and helps prison staff to care.
"We must recognise that many prisoners are highly vulnerable and that being imprisoned is a traumatic event that can have devastating consequences without the right help and support."
A prison regime should be built around a normal life, the report states. People in prison should be able to get up, have a shower and breakfast, occupy themselves productively, socialise and exercise, and go outdoors.
The report calls for the revised Incentives and Earned Privileges (IEP) scheme, introduced in prisons in November 2013 by the then Secretary of State for Justice, Chris Grayling, to be scrapped as "prisoners are being deprived of valuable coping mechanisms at a time when they most need it".