Communities Secretary Eric Pickles said he was "very sorry" to hear about the resignation of Immigration Minister Mark Harper.
Mr Harper resigned after discovering the cleaner he employed was in the UK illegally.
"I'm very sorry to hear about Mark Harper. He was a very good administer. I've known him a long time but I recognise the Prime Minister has accepted the resignation," Mr Pickles told ITV News.
"My best wishes go to him and his family."
More top news
Sydney siege victim Katrina Dawson was killed by police bullet fragments, an inquest has heard.
Experts say a trial into an early Ebola vaccine shows it is safe, but did not perform as well as had been hoped.
Frequent snowfall expected across much of the north this evening and strong northeasterly winds will make it feel noticeably cooler.