Theresa May has come under further pressure to drop the UK government's controversial "tens of thousands" net migration pledge after official data released on Thursday (1 December) showed it remained three times higher than the target.
Labour's shadow home secretary said the Conservatives have "eroded public trust" with the promise.
Diane Abbott issued the warning after the Office for National Statistics (ONS) said net migration to the UK hit 335,000 in the year to June, near the record high of 336,000.
"The Tories made a promise to the British people on net migration that they knew they could never keep, eroding public trust," she said. "But rather than learn from her mistakes as Home Secretary, May now seems committed to repeating them."
Abbott, who also serves as Labour's immigration spokesperson, criticised the prime minister after it emerged that the Home Office, under May's watch, pushed for the children of illegal immigration to be put to the bottom of the list for school places.
The leaked papers seen by the BBC also suggest that the Home Office wanted schools to carry out passport checks before accepting new pupils.
"We now know at the same time she was cutting the border force, she tried to force schools into objectionable schemes that would hurt children in a failed effort to meet that targets," Abbott added. "We should welcome overseas students and the contribution they make to our universities and wider society, and yet the Tories seem determined to discourage them to try and reach their foolish target.
"Rather than making unworkable promises or forcing schools to act as border guards, Labour will have a fair migration policy that benefits us all."
But Labour faces its own row over immigration policy. Some backbench MPs, such as Chuka Umunna, have called for reforms to the free movement of people from the EU. "I genuinely do believe that you cannot have the free movement of people in the same way as the EU was created, where you had six nations with not too similar economies," he said in February.
New Ukip leader Paul Nuttall has promised to target Labour seats in the north of England on the issue after a number of the party's heartlands backed a Brexit in the EU referendum.
A government spokesperson said: "It is only right that any Government looks at a range of options when considering policy options, but ultimately it is for ministers to decide which policies are taken forward.
"We are building an immigration system that works in the best interests of the British people and ensures that only those with a right to be in the UK can live and work here."