From the BBC sitcom 'The Fall and Rise of Reginald Perrin' starring Leonard Rossiter. A story about a man going through a mid-life crisis resulting in a breakdown where he leaves his clothes and a suicide note on a beach to give the impression he's dead whereas in reality he starts a whole new life.
Doing a Reggie means to give up on trying to solve an overwhelming situation and pretend it never happened.
Ted: The business is in trouble, Jim. We keep losing clients, the bills are piling up and the accountants have made a complete mess of our tax returns for the past ten years. We owe a lot of money to a lot of people. What are we going to do?
Jim: To be honest, Ted, I'm seriously thinking about doing a Reggie and just file for bankruptcy.