Some 27 inmates have now tested positive for coronavirus in 14 different prisons.
The number of cases, which the Ministry of Justice (MoJ) said was accurate as of 1pm on Thursday, jumped up by eight in 24 hours.
Earlier this week, the department confirmed two prisoners who had the virus had died.
The news comes as campaigners signed an open letter to the Prime Minister, Justice Secretary, Home Secretary and other ministers to call for the Government to take “urgent life-saving steps to immediately reduce” the number of people in prison, young offender institutions, secure training and immigration detention centres.
Jails in England and Wales were put on immediate lockdown on Tuesday with all visits cancelled as it emerged thousands of staff were in self-isolation.
Jo Farrar, chief executive of the Prison and Probation Service, told the Commons Justice Committee that around 4,300 prison and probation staff overall were self-isolating.
Some 3,500 were prison staff – representing about 10% of the workforce.
The latest figures, released by the MoJ on Friday, confirmed five prison staff have now tested positive for Covid-19, each in separate jails.
There have also been four prisoner escort and custody services staff who have tested positive, as well as around eight probation staff.
Around 50,000 protective masks have been delivered for staff to use and a ban on bringing hand sanitiser into the prison had been lifted.
Justice Secretary Robert Buckland has hinted he may have to consider some forms of early release for prisoners in a bid to ease pressure on jails during the crisis.
In a letter sent to political leaders on Friday – which has been signed by more than 100 campaigners – Deborah Coles, the director of the charity Inquest and Kate Paradine, chief executive of Women In Prison, made calls to to “drastically reduce the prison population and save lives both in and outside of prison”.
The letter said: “People in prison are already dying.
“Many detention settings already have the virus within their walls, with thousands of frontline staff self-isolating.
“Astonishingly, people continue to be processed through a justice system despite the known dangers.
“A failure to act, and release people now, will result in an increased risk to us all.”
The Government has a “legal and moral obligation” to protect the lives of people who have been detained “from a foreseeable danger to their health”, the letter said.
It cited plans in Iran, Ireland and US to release prisoners – saying there was a “blueprint” for the UK to follow suit.
It added: “It is clear that keeping people in prison and detention during this pandemic threatens the lives of prisoners, staff, healthcare workers – and the public health at large.”