Swings Both Ways, Williams' follow-up to 2001's Swing When You're Winning, also features collaborations with Rufus Wainwright and former The X Factor U.K. contestant Olly Murs.
Williams says, "I always knew I'd do another swing album and I think now is the perfect time to do it. The album this time is a definite ode and a loving glance towards a period on the planet that I was never invited to 'cause I wasn't there."
Williams' track with Murs is a cover of I Wanna Be Like You from classic Disney movie The Jungle Book, while Allen appears on Dream a Little Dream.
Swings Both Ways is due to hit shelves in November (13).