Former Chancellor Ken Clarke has accused the Vote Leave campaign of "Donald Trump type nonsense".
Speaking on a special debate on BBC One in the East Midlands, the Rushcliffe MP said leave campaigners were trying to scare voters about immigration.
Leicestershire MP Andrew Bridgen said wages in the UK were a huge draw for Eastern European migrants.
He added that if the UK voted to leave the EU, wages would increase for the lowest paid.
Conservative MP Mr Clarke said the UK needed EU migrants to fill jobs and that leaving the union would have no impact on people coming from "Syria or Afghanistan."
"We have to take some of those people. I think we're under a moral obligation to take some of them... but that's up to the British Government. You leave the EU and it makes no difference.
"The Leave people have no policy at all - they are just frightening you that there are lots of rapists and murderers and child molesters coming in unless we seal our borders. This is Donald Trump type nonsense."
But Mr Bridgen, Conservative MP for North West Leicestershire, said the "disparity in income" across Europe needed to be considered.
"We've brought in the national living wage. It's now £7.20 and will be £9 by 2020," he said. "That will be twice the minimum wage in Poland, three times the minimum wage of Romania and six times the minimum wage of Bulgaria."
"That's a huge draw factor for anyone to come to this country. As Stuart Rose said - who is nominally the leader of the remain campaign - that if we left the EU, wages of the poorest people in our country would rise."
EU referendum issues guide: Explore the arguments
A referendum on 23 June will decide where Britain should leave or remain.
- Better In or Out? A BBC East Midlands Today Referendum Special will be shown at 22.35 on BBC One in the East Midlands.