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Former Labour leadership contender Andy Burnham, suggested that a failure to deal with people's concerns about immigration was risking violence.
"It is time for many of us on this side of the House to confront a hard truth," he told the Commons, during an opposition debate on Brexit.
"Our reluctance in confronting this [immigration] debate is undermining the cohesion of our communities and the safety of our streets.
"I am no longer prepared to be complicit in that."
He added that immigration numbers needed to fall because "there is nothing socialist about open borders." The free movement of people within the EU had been "defeated at the ballot box and is no longer an option," he said.
Burnham claimed that the large influx of EU migrants was "not working for the most deprived areas of our country" and suggested that it had "made life more difficult where it is already hardest".
He added that the European left must "break out of its paralysis" on talking about immigration due to "the fear of being labeled as pandering".
His speech was praised as "refreshing" by Conservative MP Bernard Jenkin.
"I found the right honourable gentleman for Leigh's speech somewhat refreshing and I would submit that democracy is an awesome thing. When the tide turns in the minds of the voters then it is refreshing to see the tide turning in the minds of their representatives as well."