After the columnist called Allen an "over-privileged cry-baby" in a piece about Cheryl Cole, Allen responded on Twitter, calling Burchill a "bitter old troll" and "a bit of a self-loather".
Burchill has now told the Evening Standard: "For someone who doesn't want to be famous any more she spends a lot of time reading about herself and tweeting.
"It was partly over Cole but partly because Allen had said some ignorant s**t about the working-class and I wrote what a nerve she had as a public school mockney. Oooh, I do love a scrap."
Of the suggestion that she is self-loathing, Burchill replied: "No, Lily, dear. I Love me. I Loathe you! And BTW being called self-loathing by you is like being called fat by Dawn French. Clown!"
The writer also claimed that Allen's mother once asked her to stop picking on her daughter.
Allen recently confirmed that she still wants to be famous and added that she never said she was retiring from showbusiness.