According to Ms Cooper, the number of such visas has gone up by 30,000 a year since the election, and no checks are being made on whether students study or overstay.
- Stronger checks on shorter-term student visitor visas
- "Faster, stronger enforcement" when illegal immigrants are found
- Unannounced border agency inspections, carried out by officers with arrest powers, for employers and colleges and exit checks at borders
- More prosecutions and higher fines for paying less than the minimum wage
- Measures to tackle "gangmasters" employing illegal migrants in the social care, hospitality and construction industries
- A ban on housing workers in over-crowded accommodation
More top news
The family of a World War One hero whose bravery won him a Military Cross have condemned thieves who stole the medal from a cathedral.
Scottish leader Johann Lamont's resignation highlights the post-referendum divisions.
The remaining X Factor contestants face the judges tonight - with an exit predicted for at least one member of boy band Stereo Kicks.