But Ofcom has said after assessing the complaints it has decided not to launch a formal investigation as the comments were brief and not unexpected from Allen.
It added that LBC should take greater care to protect the mental health of young people in future.
A spokesperson for the media watchdog said in a statement: "We have provided guidance to LBC to take greater care in future.
"Given societal concerns about body image pressures on young people, the presenter's criticism of a young woman's appearance could have led to an adverse effect on wellbeing and mental health.
"But given the brevity of the comments and the likely audience's expectations of this provocative presenter and programme, we will not be pursuing further."
Allen said in October of 19-year-old Tilly - daughter of chef Gordon Ramsay - appearing on Strictly: "She can't bloomin' well dance, I'm bored with her already.
"She's a chubby little thing isn't she, have you noticed? Probably her dad's cooking I should imagine."
The CBBC presenter hit back on Instagram: "I try not to read and listen to comments about negativity however recently being called out on a national radio station by a 67-year-old man is a step too far.
"Steve – please feel free [to] voice your opinions, however I draw the line at commenting on my appearance.
"I won't tolerate people who think it's okay to publicly comment and scrutinise anyone's weight and appearance."
It has since been reported that Allen - LBC's longest-serving presenter - has since reached out to Ramsay to issue a personal apology.
Neither of them have commented on the matter since.
Watch: Who is Tilly Ramsay?