He said he was "on top of the world" to be given a second chance and join the 10 acts who are already through to the finale of the ITV show on Saturday night.
Clegg follows in his father's foosteps as he had been a contestant on TV talent show New Faces in the 1980s with his own mimicry.
In his audition the cruise entertainer and panto performer did a Celebrity Big Brother-themed act which included an impression of programme boss Simon Cowell.
He missed out on a place in the final after the judges' decision went to deadlock, but he is now back in the running for the £250,000 prize and a chance to take part in the Royal Variety Performance.
Clegg said: "My dad is absolutely over the moon. He's so made up for me. Hopefully he'll be able to come and see me perform on Saturday."