Hopkins, 38, who has become known for venting unpopular opinions, criticised the Somewhere Only We Know singer, 28, in a rant for Heat magazine.
"I quite liked her when she was singing and kind of interesting and then she went off to tell us all about being a mother," she said.
"She was removing herself from the spotlight because she wanted to be a mother and that largely involved gaining two stone and looking pretty hideous.
"So then she decided that was boring and now she wasn't going to be a mother any more, she was going to be a singer.
"Like Peaches (Geldof), she is just famous for having a famous dad."
Allen, whose father is the actor Keith Allen, reacted with fury on Twitter, writing: "Katie Hopkins: I am not famous for having a famous dad, I doubt that most of my fan base have a clue who my father is."
The singer, who lost a son six months into a pregnancy in 2010, added: "Yes, after tragically losing a child so late into my pregnancy I may have gained a few pounds. I am one of many that find comfort in food."
Allen, who went on to have two daughters, added: "The two pregnancies that followed were terrifying because of what had happened before and I was pretty much on bed rest for 20 months.
"I wasn't exercising because I didn't want to take any risks, and, funnily enough, the survival of my children felt more important than being thin.
"Can somebody tell me what Katie Hopkins does except go on telly slagging off girls half her age?
"PS: Katie, looks are obviously so important to you. There's always plastic surgery ya know. Maybe they could sew your mouth up while they fix the rest of you."
The Smile singer told her fans that she was deleting her tweets.
"Sorry about that, but my babies are a touchy subject and I gave her exactly what she wanted by responding," she said. "I am now going to delete it all."
Hopkins called US celebrity Kim Kardashian "one large bottom" and Kelly Osbourne a "purple-headed dwarf" in the filmed rant on Heatworld.com.