The general consensus seems to be that it's not hugely important to read the books in a certain order, but if you must, there are two ways to do so. You can either stick to the order in which they were originally published, or you can work your way through the books in a particular trilogy or series.
Note that the the bracketed terms after the listings are links to Amazon where you can purchase the books (PB) = Paperback, (HB) = Hardback, (TPB) = Trade Paperback, (CD) = Audio CD, (AC) = Audio Cassette (DA) = Ducks Arse, I mean er Digital Audio of course. An asterisk (*) indicates a full cast radio production.
N.B. a small percentage of the purchase price of the books will go to the club if you use these links.

By Publication Date:

• The Antipope (1981) (PB) (CD)*
• The Brentford Triangle (1982) (PB)
• East of Ealing (1984) (PB)
• The Sprouts of Wrath (1984) (PB)
• Armageddon: The Musical (1988) (PB)
• They Came and Ate Us (Armageddon II: The B Movie) (1991) (PB)
• The Suburban Book of the Dead (Armageddon III: The Remake) (1992) (PB)
• The Book of Ultimate Truths (1993) (PB)
• Raiders of the Lost Car Park (1994) (PB)
• The Greatest Show Off Earth (1994) (PB)
• The Most Amazing Man Who Ever Lived (1995) (PB)
• The Garden of Unearthly Delights (1995) (PB)
• A Dog Called Demolition (1996) (PB)
• Nostradamus Ate My Hamster (1996) (PB)
• Sprout Mask Replica (1997) (PB)
• The Brentford Chainstore Massacre (1997) (PB)
• The Dance of the Voodoo Handbag (1998) (PB)
• Apocalypso (1998) (PB)
• Snuff Fiction (1999) (PB)
• Sex and Drugs and Sausage Rolls (1999) (PB)
• Waiting for Godalming (2000) (PB)
• Web Site Story (2001) (PB)
• The Fandom of the Operator (2001) (PB)
• The Hollow Chocolate Bunnies of the Apocalypse (2002) (PB) (HB) (CD) (AC)
• The Witches of Chiswick (2003) (PB) (HB)
• Knees Up Mother Earth (2004) (PB) (HB)
• The Brightonomicon (2005) (PB) (HB) (TPB) (CD)* (DA)*
• The Toyminator (2006) (PB) (HB) (TPB)
• The Da-da-de-da-da Code (2007) (PB) (HB) (TPB)
• Necrophenia (2009) (PB) (HB) (TPB)

By Series:

The Brentford Trilogy

• The Antipope (1981) (PB) (CD)*
• The Brentford Triangle (1982) (PB)
• East of Ealing (1984) (PB)
• The Sprouts of Wrath (1984) (PB)
• The Brentford Chainstore Massacre (1997) (PB)
• Sex and Drugs and Sausage Rolls (1999) (PB)
• Knees Up Mother Earth (2004) (PB) (HB)
• The Brightonomicon (2005) (PB) (HB) (TPB) (CD)* (DA)*

The Armageddon Trilogy

• Armageddon: The Musical (1988) (PB)
• They Came and Ate Us (Armageddon II: The B Movie) (1991) (PB)
• The Suburban Book of the Dead (Armageddon III: The Remake) (1992) (PB)

Cornelius Murphy Novels

• The Book of Ultimate Truths (1993) (PB)
• Raiders of the Lost Car Park (1994) (PB)
• The Most Amazing Man Who Ever Lived (1995) (PB)

The Trilogy That Dare Not Speak Its Name

• Sprout Mask Replica (1997) (PB)
• The Dance of the Voodoo Handbag (1998) (PB)
• Waiting for Godalming (2000) (PB)

The Witches Trilogy

• The Witches of Chiswick (2003) (PB) (HB)
• Knees Up Mother Earth (2004) (PB) (HB)
• The Brightonomicon (2005) (PB) (HB) (TPB)

Eddie Bear Novels

• The Hollow Chocolate Bunnies of the Apocalypse (2002) (PB) (HB) (CD) (AC)
• The Toyminator (2006) (PB) (HB) (TPB)

Standalone Novels

• The Greatest Show Off Earth (1994) (PB)
• The Garden of Unearthly Delights (1995) (PB)
• A Dog Called Demolition (1996) (PB)
• Nostradamus Ate My Hamster (1996) (PB)
• Apocalypso (1998) (PB)
• Snuff Fiction (1999) (PB)
• Web Site Story (2001) (PB)
• The Fandom of the Operator (2001) (PB)
• The Da-da-de-da-da Code (2007) (PB) (HB) (TPB)
• Necrophenia (2009) (PB) (HB) (TPB)