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
A football-starved community in Argentina has found a way to play the game they love in a time of coronavirus.
The plane hit an area of water away from the expected and standard flight path, crashing in a near-vertical position.
Quarantine restrictions are being amended, allowing people to travel without needing to self-isolate on their return.