The 74-year-old was said to be “in a bad way” after collapsing twice at Littlehey Prison in Cambridgeshire, where he was serving an eight-year jail sentence for historic sex offences.
A spokesman for the Ministry of Justice confirmed Clifford died in hospital on December 10.
“As with all deaths in custody, there will be an investigation by the independent Prisons and Probation Ombudsman,” the spokesman said.
“Our condolences are with Mr Clifford’s family at this difficult time.”
His daughter, Louise, 46, told the Mail on Sunday that Clifford first collapsed in his cell on Thursday when he was trying to clean it.
“It was just too much,” she said.
She said he collapsed again the next day and was unconscious for several minutes, and after seeing a nurse was transferred to a local hospital where he suffered a cardiac arrest on Friday.
Following this she said he was in a critical care unit and described him as being in a “bad way”.