Rex Features
The Girls Aloud singer told Glamour that she and Allen had finally run into each other after an on-off war of words in recent years.
Cole said: "I met Lily for the first time last week. I gave her a hug and said, 'Nice to meet you'. To which she said, 'There is no beef'.
"Then I hear she was in the press room taking the piss and I thought, 'She's a little girl but I'm a 26-year-old woman and I'm not at school anymore'."
Last month, Cole said that she would never forgive Allen for her "awful" remarks about her husband Ashley and bandmate Nicola Roberts.
