Investigations have been launched into the deaths of two prisoners within 48 hours at HMP Lewes.
The Ministry of Justice said Neville McNair died on Saturday, a day before his 52nd birthday.
Ricky Coombs, 25, died on Monday of injuries which are believed to have been self-inflicted.
A Prisons Service spokesman said: “As with all deaths in custody there will be an independent investigation by the Prisons and Probation Ombudsman.
“Our condolences are with Mr Coomb’s and Mr McNair’s family and friends at this difficult time.”
HMP Lewes, in East Sussex, is a category B men’s prison with a capacity of 617 inmates.
Its most recent inspection in 2016 found it was overcrowded, holding 640 prisoners, a “substantial number” of whom were awaiting trial or sentence.
A report by HM Chief Inspector of Prisons said more than a quarter of prisoners at Lewes reported feeling depressed or suicidal.
It also found some staff did not have anti-ligature knives and “could not assure us that they would act appropriately in the event of a serious self-harm incident."
In April, campaigners warned of a “system in crisis” as self-harm in UK prisons reached a record high.
More than 11,600 prisoners harmed themselves in jails across England and Wales during 2017, the equivalent of one every 12 minutes.
