- 1977 - My Aim Is True (UK #14, US #32)
- 1978 - This Year's Model (UK #4, US #30)
- 1979 - Armed Forces (UK #2, US #10)
- 1980 - Get Happy!!(UK #2, US #11)
- 1981 - Trust (UK #9, US #28)
- 1981 - Almost Blue (UK #7, US #50)
- 1982 - Imperial Bedroom (UK #6, US #30)
- 1983 - Punch the Clock (UK #3, US #24)
- 1984 - Goodbye Cruel World (UK #10, US #35)
- 1986 - King of America (UK #11, US #39)
- 1986 - Blood and Chocolate (UK #16, US #84)
- 1989 - Spike (UK #5, US #32)
- 1991 - Mighty Like a Rose (UK #5, US #55)
- 1993 - The Juliet Letters (UK #18)
- 1994 - Brutal Youth (UK #2, US #34)
- 1995 - Kojak Variety (UK #21)
- 1995 - Deep Dead Blue
- 1996 - All This Useless Beauty (UK #28, US #53)
- 1998 - Painted from Memory, with Burt Bacharach (UK #32, US #78)
- 2001 - For The Stars , with Anne Sofie Von Otter
- 2002 - When I Was Cruel (US #20)
- 2003 - North (UK #44, US #57, US Traditional Jazz #1)
- 2004 - Il Sogno
- 2004 - The Delivery Man (US #40)
- 2005 - Piano Jazz: Costello/McPartland
- 2006 - My Flame Burns Blue
- 2006 - The River in Reverse , with Allen Toussaint
- 2008 - Momofuku
- 2009 - Secret, Profane & Sugar Cane
- 2010 - National Ransom
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