Prison suicides in England and Wales have risen to the highest level for seven years with 82 prisoners taking their own lives last year, according to new figures.

The Howard League for Penal Reform said that Ministry of Justice figures to be published next week will confirm the rise in the prison suicide rate. The justice ministry notifications include the deaths of 14 people between the ages of 18 and 24.

The figures show that the highest number of deaths occurred at two of the biggest jails. Four people took their own lives at Wandsworth prison, south London, last year. The jail currently holds 1,633 prisoners in accommodation designed for 943. Four people also took their own lives at Elmley, Kent, which holds 1,231 inmates in a jail also built for 943.

The figures show that in total there were 235 deaths inside prisons in 2014, with more than 120 dying from natural causes, and a further 24 deaths yet to be classified. There have been two alleged murders. The first happened in Cardiff prison last March and the second in Altcourse prison in November.

Frances Crook of the Howard League for Penal Reform said the figures hid the true extent of misery inside prisons and for families: “Hard-pressed prison staff have to save lives by cutting people down almost every day and without this the death toll would be even higher,” she said.

“It is evident that people are dying as a direct result of the cuts to the number of staff, particularly more experienced staff, in every prison. The government has chosen to allow the prison population to increase whilst it cuts staff, and that has led to an increase in people dying by suicide,” said Crook.

The prisons minister, Andrew Selous, responded saying: “Every death in custody is a terrible tragedy. We remain focused on doing all we can to prevent them.”

But he went on to accuse the Howard League of using the loss of lives for their own campaigning purposes: “They are deliberately misrepresenting the situation in our prison for their own ends. This helps no one – least of all the vulnerable individuals in prison whose wellbeing is the absolute priority of prisons staff and ministers alike,” he said.

Justice ministry officials said they can’t comment on unverified figures but the official statistics will be published next week.

Ministers have repeatedly insisted that there is no evidence directly linking staff levels, type of prison or overcrowding to the number of prison suicides and the rate of self-inflicted deaths remains below the levels seen in 2005 and 2007.

The justice secretary, Chris Grayling, has repeatedly said it has not so far proved possible to establish a pattern or any simple explanation for the factors that lie behind the rise. He set up an independent review into the deaths of young adult prisoners aged 18 to 24 which is due to report in March.

But the Prison Governors Association warned in October that prisons were facing a “toxic mix” of increasing prisoner numbers, chronic staff shortages and rising violence that was driving them towards instability. The prison governors reported that although the number of deaths in custody petered out “at the back end of last summer” they had since started to rise again.

A Guardian investigation also identified distinct themes in many of the self-inflicted deaths, including failures in the assessment of risk in the face of obvious warning signs, a lack of training for prison staff, inadequate monitoring once risk was identified and insufficient communication with families.