A second inmate at Pentonville prison has been arrested after a knife attack in the jail that left one prisoner dead and two others in a critical condition.

The 26-year-old suspect was taken to a north London police station, where a 34-year-old was already being held for questioning by detectives from the Metropolitan police’s homicide and major crime command, police said.

Officers and paramedics were called to the prison at 3.30pm on Tuesday, where three men had suffered stab wounds. At 4.25pm, one inmate, in his 20s, was pronounced dead at the scene.

The two other victims, aged 21 and 30, remained in a critical condition in an east London hospital.

On Wednesday morning, police said they were in the process of informing the next of kin of the dead man, who had not yet been formally identified. “Further inquiries into the incident continue,” the Met said in a statement.

Visitors queuing inside the prison spoke of their safety concerns. A woman visiting her 21-year-old son initially feared he could have been the victim. She said: “My son is 21, I haven’t felt the same since I heard the news.

“As a mother everyone tells you at least you know where he is and he is safe – but actually he’s not safe, is he? No matter their age or what they have done, no one deserves to die in prison. It is supposed to be a place of safety.”

Another woman said: “It shouldn’t be allowed to happen anywhere, let alone in prison. It’s obviously not safe in there.”

The Prison Governors Association (PGA) on Wednesday renewed calls for a public inquiry into the state of jails in England and Wales. The union said government cuts to staff and resources meant the incident at Pentonville was “no massive surprise”.

Recent statistics published by the Ministry of Justice showed there were 100 apparently self-inflicted deaths in the year to March, the highest for more than a decade. There were more than 20,000 assaults – 2,813 deemed “serious” – in the 12 months to December, a rise of 27% year-on-year, and nearly 5,000 attacks on staff, a jump of more than a third compared with 2014.

John Attard, national policy officer at the PGA, said: “It is no secret that we have had concerns about cuts and resources over the last four years. The Ministry of Justice statistics paint a very grim picture indeed.”

Referring to Tuesday afternoon’s incident as a “tragedy”, he said: “The prison service paid staff to leave. The years of experience, the mentoring, the sharing of their experiences – a lot of that has been lost, and it is showing. It’s why we need an inquiry into this.”

Speaking outside the prison gates, Attard added: “We called for an independent public inquiry a week ago. The reduction in staffing is a key factor, there’s no doubt about that, but synthetic drugs also had some part in that. What we would like to see is a regime that can be managed safely with the right number of staff.”

He said the prison was one of the most dangerous in the country and would be at maximum security while it was searched. “Pentonville is one of the busiest prisons and it will, by its very nature, be one of the most violent prisons as well,” he said.

“Right now it will be on lockdown. With additional support from other prisons, all of the prison will be searched and there will be a hunt for any weapons, mobile phones, drugs and tools.”

Home-made weapons are commonly seized from prisoners but are hard to detect, he said. “Prisoners frequently make, and prison officers frequently retrieve, home-fashioned weapons and they tend to be toothbrushes with razor blades melted into the end of them.

“It’s almost impossible to stop and particularly more difficult when there are less staff to do it,” he said.

The Prison Officers Association (POA) said it “once again” had serious concerns following the incident. In a statement, the union said: “The actions of the staff at Pentonville maintained good order and discipline and prevented this situation escalating.”

The POA said it would not make further comment “other than to say the unprecedented rise in violence in all of our prisons must not be underestimated”.

It added: “We now ask for the Ministry of Justice to fully investigate this matter and the underlying problems within the prison estate.”

Former prisons minister Andrew Selous insisted money was being invested in recruiting new staff and building modern jails.

“What has happened is horrendous. I have met the parents of prisoners who have been murdered and it is horrific and my deepest sympathy goes out to all those affected,” he told BBC Radio 4’s Today programme.

“The government absolutely gets the seriousness of the violence issues, there is a huge amount of work being done to reduce violence.” But he said: “We absolutely need more officers on the wings,” adding that ministers had promised extra funding.

Selous said Pentonville was a very old prison and the government’s plans for new jails would help.

In July last year, Michael Gove, then justice secretary, described Pentonville as“the most dramatic example of failure within the prison estate”.

Opened in 1842, the category B prison holds 1,200 inmates, despite a nominal capacity of 900. A report by the chief inspector of prisons last year said conditions for inmates were among the poorest in England and Wales. Drugs were easily available, cells were filthy and some inmates were locked up for up to 23 hours a day.

“On one occasion we found prisoners located in a cell with blood on the walls and door, and on another occasion with blood on the bunk bed; on neither occasion was the blood cleaned up when we raised our concerns with staff,” the report said.

The PGA recently gave a warning that cost cuts were affecting safety standards in jails.

“Our members, uniformed staff and prisoners are working and living in squalid and brutal conditions which should not be tolerated in a country that is one of the richest in the western world. If a society is judged by how it treats those it locks up, then we are in a very dark place.”