We must be clear if the police shows up with a warrant even in your country you cannot oppose the search of your home, but I don't see any report of the immigration visit to check that you live in that home with your wife and take some photos that confirm what you stated. We are well ahead of a search of your home by immigration.
However, if one day you receive a visit for a search in your home,you will also receive the documents describing the law and the reason for the search of your home, the same thing happened to the Big Joke recently.