Some 27 inmates have tested positive for coronavirus across 14 prisons, the Ministry of Justice has said.
The inmate, convicted paedophile Edwin Hillier, was serving at HMP Littlehey in Cambridgeshire.
Hillier, who reportedly had underlying health issues, died in hospital on Sunday, having been moved there from the category C male sex offenders' prison.
A second serving UK prisoner, a 66-year-old male inmate at HMP Manchester, died in hospital on Thursday after contracting coronavirus.
He had been receiving end-of-life care for an underlying health condition before he tested positive for Covid-19.
A Prison Service spokesman said: "An 84-year-old prisoner at HMP Littlehey died in hospital on March 22.
"A 66-year-old prisoner at HMP Manchester died in hospital on 26 March."
The Ministry of Justice and Her Majesty's Prison and Probation Service said the measure was to "ensure the safe and secure functioning of our prisons, while enforcing social distancing."
The Prison Officers' Association (POA) said it "praised the decision [...] to place prisons in England and Wales on immediate lockdown".