British Police

I'm not familiar with British police or their procedures. What does H-MIT stand for? In the US, police cannot investigate crimes or the individuals involved in that crime if it leads to someone they know or have a history with them. The good sergeant would never be allowed anywhere near Tommy or pay a visit to his mother, no matter what our television show or movies show on screen, it would hurt the prosecutions case, any evidence collected at the house would not be allowed into evidence because she didn't have a warrant to enter the house. She would've been removed from the case of the death of one of her staff members and placed on temporary leave and order all staff including herself to get grief counseling. Do they do the same thing there and is it just a television series idea?