Britain will need to build seven new prisons to cope with the number of migrant law-breakers set to arrive in the country by 2030, the Leave campaign claims.
Tory former cabinet minister Iain Duncan Smith insists that if current migration levels continue, and the same percentage of them commit prison worthy offences as the rest of the population, some 7,226 extra jail places will be needed.
Of these, Leave estimates that 3,993 convicts will be from the rest of the EU, and that Britain will need another seven jails the size of the 606-capacity Full Sutton prison to house them.
Mr Duncan Smith said: "Our prisons already hold over four thousand criminals from the EU, costing taxpayers more than £150 million a year.
"The problem will only get worse if we stay in the EU, especially as Turkey, Macedonia, Albania, Serbia and Montenegro join.
"Our analysis shows UK taxpayers will have to pay an extra £400 million just to keep EU criminals in jail. It will mean prisons are more crowded, less safe and less able to prevent inmates returning to crime.
"If we vote to leave, we can take back control of our borders and send EU criminals back to their own countries. We will be able to keep out terrorists and kick out criminals. We would also take back control of the £350 million we send the EU every week and spend it on our priorities instead."
The estimate is based on net migration levels from the EU continuing at a rate of 184,000 a year until 2030.
A spokesman for Britain Stronger in Europe said: "Even by their own standards, this is nasty scaremongering of the worst kind from Vote Leave.
"These made-up numbers are so baseless it's notable the current Justice Secretary, Michael Gove, won't put his name to it and instead Iain Duncan Smith has been wheeled out to blow the dog whistle."