The following BMC Australia factory document details the various production colour combinations for the Cooper S paint and trim. You'll see that BMC used codes to identify the various colour combinations.
Some enthusiasts have said their car's combination is not listed so it's likely the documents are incomplete.
The first set is for the Mark 1 and shows the first sheet for a specific configuration - monotone Burgundy paint with Doeskin trim.
The second set is for the MK II.
Attachment:
Cooper S Mark 1 Colour Combination No 61 v2.jpg
Attachment:
Cooper S Mark 1 Colour Combinations v2.jpg
Attachment:
Cooper S MK II Colour Combinations Sheet A v2.jpg
Attachment:
Cooper S MK II Colour Combinations Sheet B v3.jpg
Attachment:
Cooper S MK II Colour Combinations Sheet C v3.jpg
Attachment:
Cooper S MK II Colour Combinations Sheet D v3.jpg