Helen Mirren saw the picture on Clive Owen's dressing table. It showed him as a child with his mother, a mother CO believes is dead. HM realised it was a picture of her and her child and that CO was her son by Michael Gambon'c character.
MG had a history of impregnanting the women on the staff and then forcing them to either give up their children or leave his employ in disgrace (and with a bad reference, they would find it hard to find more employment).
HM realises that CO will kill MG, and not wanting her son to suffer the consequences of this crime, kills him herself.