Freddie Starr and Clifford, who were arrested by detectives investigating the Jimmy Savile sex abuse scandal, have been rebailed until next year.
Police said comedian Starr and publicist Clifford have been rebailed to return on dates in February and March pending further inquiries.
Starr, 69, was arrested in Warwickshire on November 1 as part of Operation Yewtree, the investigation into allegations of sex abuse surrounding Savile and others. He had been publicly implicated in the Savile scandal but strongly denied any accusations.
PR guru Clifford was arrested on December 6 at his Surrey home on suspicion of sexual offences. He described the allegations as "damaging and totally untrue".
A Scotland Yard spokesman said: "Two men arrested as part of Operation Yewtree have been rebailed to return pending further inquiries.
"A man in his 60s ('Yewtree 2'), who was arrested on November 1, has been rebailed to return on a date in March pending further inquiries.
"A second man in his 60s ('Yewtree 6'), who was arrested on December 6, has been rebailed to return on a date in February pending further inquiries."
Former pop star Gary Glitter and a man in his 70s, reported to be former television producer Wilfred De'Ath - also among those arrested as part of Operation Yewtree - were re-bailed by police last week.
Glitter, 68, whose real name is Paul Gadd, was the first person to be detained on October 28, and a man reported to be De'Ath, a former BBC employee who once produced a radio show presented by Savile, was arrested at his home in Cambridgeshire on November 11. Both were re-bailed to return on dates in February 2013.
Last week police said that a total of 31 allegations of rape have been made against Jimmy Savile so far.