The illegal workers were arrested in enforcement operations on businesses and private addresses across England, Wales and Scotland.
These businesses now face fines of up to 10,000 pounds for each illegal worker, unless they can prove that they carried out the correct pre-employment checks, the agency said.
In Edinburgh, three Indian men and six women were arrested following an investigation into a legal advisor.
The advisor, Harpreet Dhall, was jailed for 6 years earlier this year for helping to submit applications for work visas by creating false documents and employment histories for his clients.
In Aberdare, South Wales, a man was found working in a shop in breach of the conditions of his student visa.
Twelve Indian men were arrested in co-ordinated enforcement operations on a national car parts company in Tamworth, Staffordshire and Wembley.