The men were due to answer police bail in January, but have now been told by officers from Scotland Yard’s Operation Yewtree, that they do not need to return until two months later.
They were both held in south London in October over alleged sexual offences that are not linked to disgraced DJ Savile.
Scotland Yard did not name the men, but said: “Two men arrested as part of Operation Yewtree have been bailed.
“On October 29 officers from Operation Yewtree arrested a 64-year-old man (Yewtree 15) and 74-year-old man (Yewtree 16) in connection with the investigation.
“Both were arrested at separate addresses in south London on suspicion of sexual offences and taken into police custody.They were bailed to return in January 2014 pending further inquiries but have now been re-bailed to return pending further inquiries and are next due on a date in March 2014.”
Gambaccini, 64, denied the allegations after his arrest.
He said in a statement: “On Monday night, October 28, I attended an excellent production of the Kander and Ebb musical, the Scottsboro Boys, at the Young Vic theatre.
“It concerned a group of black men in Alabama in the 1930s who were falsely accused of sexual offences.
“Within hours, I was arrested by Operation Yewtree. Nothing had changed, except this time there was no music.”
His spokesman confirmed that the veteran broadcaster had spoken to police and said: “He denied all allegations.”
Gambaccini, who hosts a weekly show on BBC Radio 2, was highly vocal last year in the wake of Savile’s years of sexual abuse being made public, and said it was known among BBC staff that the late presenter targeted vulnerable, “institutionalised” young people.
He also spoke of rumours that his former BBC Radio 1 colleague had been a necrophiliac.
So far 16 people have been arrested as part of Operation Yewtree, seven of whom have been told they will face no further action.
Four have been charged in separate cases - DJ Dave Lee Travis, veteran performer Rolf Harris, PR guru Max Clifford and former driver David Smith, who has since died.
A further five remain on police bail - former pop star Gary Glitter, comedian Freddie Starr, ex-Radio 1 DJ Chris Denning, Gambaccini and the 74-year-old man.