Both of the men, who were being held at HMP Wakefield, were advised to shield on several occasions as they had underlying health conditions, but they refused.
Michael Preston 68, died on November 7 in 2020 and James Palmer, 74, died on December 6.
An investigation conducted by the Prisons and Probation Ombudsman found that Mr Preston was the first inmate at the prison to die from Covid-19 and five more have died since then after catching the virus.
He was first remanded in custody for sexual offences in 2009 and then handed a life sentence the following year.
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Mr Preston suffered from chronic obstructive pulmonary disease (COPD), high blood pressure and diabetes, but decided to stop attending doctors appointments in May 2020.
Due to his health issues, he was deemed to be high-risk and advised by a prison nurse to move to a shielding unit on three occasions, but he refused and signed a disclaimer.
He was taken to hospital by ambulance on the morning of October 19 after prison officers found that he was struggling to breathe in his cell.
He was treated at the intensive care unit and then released on temporary licence on October 27, but his health deteriorated and he died at 8.16pm on November 7.
Mr Palmer, who was sentenced to life imprisonment for wounding with intent in 1995, was also suffering with several health problems, including hypertension and diabetes.
In May 2019, he had a heart attack and then required treatment for a blocked artery in his heart. He was also put on medication to treat atrial fibrillation.
After initially agreeing to shield in April 2020, he decided to stop and return to his day-to-day activities but he then caught the virus in November.
On December 6, he collapsed in his cell and he was taken to hospital via ambulance, but he died later that day.
His son asked why he had not been released on compassionate grounds before his death and the prison governor stated that is only granted in exceptional circumstances, including cases where an inmate is terminally ill, but Mr Palmer had not been diagnosed with a terminal condition.
In both cases, coroners recorded the cause of death as “Covid-19 pneumonia”.
Prisons and Probation Ombudsman investigators found that staff at the high-security prison, which is nicknamed Monster Mansion because it has held several high-profile criminals, had taken steps to protect inmates from the virus.
All inmates arriving at the prison had to quarantine for 14 days, and protective isolation cells for anyone with Covid-19 and shielding units for high-risk prisoners were set up.
According to the Ministry of Justice (MoJ), it can hold up to 750 men and each is given their own room.
The MoJ has been approached for a comment.