The woman was sedated and then had the girl taken out of her body after authorities in Essex, eastern England, obtained a court order, the Telegraph newspaper said, citing her lawyers.
The authorities said the woman had had a mental breakdown and it acted in the best interests of the child, which is now 15 months old, the paper said.
The Italian mother has now launched a legal battle for the child, which is being put up for adoption by the social services, it said.
"I have never heard of anything like this in all my 40 years in the job," her lawyer, Brendan Fleming, told The Telegraph.
The woman had flown into Britain in 2012 for a two-week Ryanair training course at Stansted airport north of London when she suffered a panic attack, which her family believe was due to her failure to take medicine for a bipolar condition, the newspaper said.
She has since launched legal action in Britain and Italy for the return of her daughter but has been told that the child will be placed for adoption.
A British lawmaker, John Hemming from the Liberal Democrat party, will raise the case in parliament this week, the newspaper said.
It quoted Essex council as saying it did not comment on ongoing cases.