The three words that complete the quotation "You have no hope of ________, ________, ________, Mrs Birling." from J.B. Priestley's play "An Inspector Calls" are "not denying it." The full quotation is: "You have no hope of not denying it, Mrs Birling." This line is spoken by the Inspector to Mrs Birling, indicating she cannot hope to escape admitting her responsibility in the situation being investigated. It emphasizes the moral accountability she faces despite her attempts to refuse or deflect blame.

This captures Mrs Birling’s cold and unrepentant attitude, as well as the Inspector's role in pressing the characters to acknowledge their part in the consequences of their actions involving Eva Smith/Daisy Renton.

Thus, the completed quotation reads: "You have no hope of not denying it, Mrs Birling." This reflects the crucial theme of accountability and social responsibility in the play.