One in eight prisoners in England and Wales have tested positive for Covid-19 since the pandemic began, latest figures show, after a 70% surge in the number of cases recorded behind bars.

At the end of January, 10,354 prisoners or children in custody had tested positive for Covid-19 since the start of the pandemic, an increase of 4,227 cases since December, according to monthly data from the Ministry of Justice.

With a prison population in England and Wales of 78,000, this equates to roughly one in eight prisoners and compares with about one in 20 who have tested positive for the coronavirus in the wider community.

Penal reform campaigners said the figures backed the case for vaccinations for prisoners to be provided “as quickly as possible”. It is understood vulnerable prisoners are expected to be vaccinated in line with the general vaccine rollout.

Between March and January, 86 prisoners died having tested positive for Covid-19 or where it was confirmed postmortem, the figures show, up from 71 at the end of December.

There were 107 prisons or young offender institutions with positive cases in January. There are 121 jails in England and Wales.

Separate figures show a tentative decline in the rate of new positive cases in the first week of February, with 771 positive cases in the week to 8 February compared with 1,197 in the previous week.

Frances Crook, the chief executive of the Howard League for Penal Reform, said: “These figures should remind everyone that viruses can spread rapidly in confined settings such as prisons. They underline the need for vaccinations of staff and prisoners to be carried out as quickly as possible.”

David Lammy, the shadow justice secretary, said: “The government’s complacency over the coronavirus pandemic in prisons is very concerning given the fact infections are far outpacing the general population.

“More staff and inmates will die if the Ministry of Justice does not get control of the virus. Outbreaks in prisons can also overwhelm hospitals and infect the rest of the public. The government’s failure to control the pandemic in our prisons – and across the country – is putting the NHS at risk.”

The MoJ has been testing all symptomatic prisoners since April and has piloted mass testing in about one-fifth of prisons.

Restrictions in prisons broadly reflect the situation in the wider community under national lockdown. Social visits are suspended in England, except on exceptional compassionate grounds. Visits to children in youth custody will continue.

A Prison Service spokesperson said: “The most recent statistics show the number of infections in prisons has fallen for the last three consecutive weeks.”