The Creative Review blog has an excerpt from Penguin by Designers by David Pelham describing how this cover and others came about.
I came across a paperback copy of A Clockwork Orange by chance in my brother’s room, when I was much younger. And yes — it had David Pelham’s jolting cover art. I recall being very disturbed by that blank face with the sprocket eye against an alarming orange background and since then I’ve associated Burgess’s work most closely with that cover. All other covers for the book — in fact most other book covers — pale in comparison if you ask me (and apparently the book designer for the UK version of 1001 Books You Must Read Before You Die agrees). But I do like the beguiling innocence of the glass of milk on the Penguin Modern Classics version:
(Thanks to covers.fwis.com)