Robbie Williams’ Swing When You’re Winning is his best-selling album to date. Now, nearly 13 years since its release, he’s revisiting the smoothness and style of the Rat Pack generation with new LP Swings Both Ways.

Released this week, currently leading the charge in the Official Midweek Sales Chart, and featuring major league collaborators such as Lily Allen, Michael Bublé and Rufus Wainwright, it marks the latest entry in a prolific period for Williams that started with 2009’s Reality ...