The report comes after MigrationWatchUK claimed it would take 20 or 30 years to build enough social housing for illegal immigrants if there was an amnesty.
For Migrationwatch, Sir Andrew said that while the UK needed some economic migrants, there should be more restrictions on people being allowed to settle permanently.
But the lobby group MigrationWatch, which supports tighter immigration controls, has predicted that 50, 000 Bulgarians and Romanians will come to the UK every year when the restrictions are lifted.