ALDE group leader Guy Verhofstadt has claimed that Brexit will increase, rather than cut, migratory flows to the UK.
Speaking in Parliament on Tuesday, the deputy also said that a Leave vote in this month's In/Out referendum would create "enormous administrative burdens" for the 1.2 million Britons working and living in Europe.
His comments come with latest opinion polls showing a slight lead for the Leave camp ahead of the 23 June referendum.
Verhofstadt told a news conference in Strasbourg that contrary to what the Leave side has argued, migration to the UK would rise sharply if the country leaves the EU.
He said, "The Leave side have tried to use migration as a reason for exiting the EU but this ignores the reality of the situation which is that Britain will face a bigger migration problem than now if it leaves.
"Britain will be confronted with thousands and thousands of people who want to go there so, rather than limiting migration a Brexit would actually increase migration to the UK."
The Belgian MEP also warned that Britons living and working in Europe would need visas and work permits in the event of a Brexit. "This is not currently the case and it will create enormous administrative burdens," he said.
Verhofstadt, attending the last plenary before the vote, also said the debate in Britain on a possible Brexit had failed to address the "geopolitical" consequences of the world's fifth biggest economy going it alone.
He said that, along with Donald Trump and Russian President Vladimir Putin, Brexit was one of three "threats" to the Euro-Atlantic community.
"It is vitally important we talk about these things in the final days of the campaign."
Also speaking in Parliament, EPP group Chair Manfred Weber told reporters Britain would "forfeit" some of the influence it currently has if it leaves the EU.
Saying he was waiting with "bated breath" for the outcome of the vote, the German deputy said he was disappointed the debate had focused on "details", such as issues that were "a source of frustration" to the public, rather than on the "bigger picture" and matters like globalisation.
"I do not think this has been given sufficient airing in the debate," said Weber, who was speaking at a news conference at this week's Strasbourg plenary.
"Of course, the UK can choose to leave but, if it does, it cannot expect to still have the same influence."
He added, "I respect the special role the UK has carved out for itself in the EU but a Brexit would, I believe, be detrimental and that is why I hope it does not happen."
Further comment came from S&D group leader Gianni Pittella, who said he hoped to be "celebrating" a decision to remain in the EU after the vote on 23 June.
The Italian MEP added, "The British must vote for what is in their best interests but I believe this is to remain in the EU. That would be good for the UK."
Meanwhile, the secretary general of Nato on Monday warned against Brexit and moves that result in "a more fragmented security environment" in Europe.
"We don't need more instability, we don't need less cooperation in Europe," Jens Stoltenberg told an event in Brussels.