Immigration cap: Lord Bilimoria and Tory MP Mark Harper
10 December 2012 Last updated at 14:01 GMT
Immigration Minister Mark Harper said Britain was "very much open for business" and the cap on skilled workers "is not anywhere near being reached".
He was responding to claims that businesses were being hurt by a limit affecting people from outside the EU trying to get into the UK, aired in a Daily Politics film.
Crossbench peer Lord Bilimoria, the founder and chairman of COBRA beer, said Britain has "lost control of our borders" and the UK Border agency could not give a figure on the number of illegal immigrants.