There were 5,423 assaults on prison staff in the 12 months to the end of March - a rise of 40% on last year, the Ministry of Justice said.
Self-inflicted deaths in the year to the end of June were up from 82 to 105 - a rise of 28%.
Meanwhile 65 prisoners were released in error in 2015-16 - the highest total for six years.
Overall, the performance of prisons appears to have worsened, with six jails giving "serious concern" - Bristol, Doncaster, Hewell, Isis, Liverpool and Wormwood Scrubs - compared with only three in 2014-15.
Justice Secretary Elizabeth Truss said the level of violence in our prisons was "unacceptable" and highlighted the prevalence of psychoactive substances as a problem.
"I am clear that safety in prisons is fundamental to the proper functioning of our justice system and a vital part of our reform plans," she said.
"There are a number of factors including the availability of psychoactive substances in prisons which must be tackled. It will take time to address these long-standing problems. I am determined to make sure our prisons are safe and places of rehabilitation."
The government figures also revealed that:
Shadow prisons minister Jo Stevens said the figures highlighted "the absolutely unacceptable state of our prison and probation system", adding that "neither prison staff nor prisoners are safe".
"Fifteen assaults on prison staff every single day cannot continue. Prisoner suicides have increased and the number of people who've been accidentally released from prison is at a six-year high," the Labour MP added.
Andrew Neilson, director of campaigns at the Howard League for Penal Reform - a national charity that campaigns to have fewer people in prison - said the figures showed "the urgent need for prison reform".
"Prisons are not only becoming more dangerous; they are becoming more dangerous more quickly," he said.
"That more prisons have been awarded the worst-possible performance rating provides further indication of how the system is failing after years of rising numbers, chronic overcrowding and deep staff cuts."
Mr Neilson said it was "particularly shocking" to see increases in the number of women taking their own lives, adding: "The high levels of violence and deaths should shame us all, and the new secretary of state for justice and her ministers must set out concrete plans to reduce them."
Last week the Chief Inspector of Prisons, Peter Clarke, warned that jails had become "unacceptably violent and dangerous places".
In his first annual report, Mr Clarke said the "grim situation" revealed in last year's report was now "even worse" in some areas.
Assaults on prison officers in England and Wales have risen to their highest level on record, official figures show.