AP
Clifford reportedly collapsed in prison on Thursday, where he was serving an eight-year sentence for historic sex offences.
BBC News reported earlier that Clifford had suffered a heart atack following the incident on Thursday.
Clifford's daughter Louise told The Mail on Sunday that Clifford collapsed while attempting to clean his prison cell.
The Ministry of Justice told BBC News: "As with all deaths in custody, there will be an investigation by the independent Prisons and Probation Ombudsman. Our condolences are with Mr Clifford's family at this difficult time."
Clifford became famous for representing various celebrities and using unorthodox tactics to boost their public images.
One of Clifford's most audacious stunts was to encourage a 1986 Sun headline "Freddie Starr ate my hamster." Starr, who was one of Clifford's clients, initially wanted the story killed, but Clifford realised that it could result in more recognition for his client.
Clifford's other clients included "Celebrity Big Brother" winner Shilpa Shetty, David Beckham's former personal assistant Rebecca Loos, Kerry Katona, and Jade Goody.