Play the white man is a term used in parts of England meaning to be decent and trustworthy in one's actions.
The origin of the phrase is obscure. The term carries with it a reference to an obligation which many English civil administrators in the latter years of the British Empire might have considered themselves to be under: that is, the obligation to uphold respect for their county abroad by maintaining personal standards of behaviour and fairness which darker-skinned native peoples could respect. The act of calling upon someone to remember his personal moral obligations in this way is expressed in Rudyard Kipling's poem The White Man's Burden. On the other hand, the racially neutral colour white has long been associated with pureness and virtue.
A similar expression in the United States is "That's mighty white of you", meaning, "Thank you for being fair". 
In July 2013 Coronation Street featured the beginning of a storyline where character Paul Kershaw (Tony Hirst) was accused of racism by Lloyd Mullaney (Craig Charles) after using the phrase "Play the white man" during a game of darts in their local pub The Rover's Return. This sparked Paul to be accused of racism, with Lloyd's friends in the street siding with him, and both men refusing to back down due to differing interpretations of the phrase's connotations.