I'd say no hyphen is preferable nowadays. The OED entry that Lady Grey mentions in #1 states "This entry has not yet been fully updated (first published 1891)."
Given the date of the sole quotation for "clothes-peg" is 1825, I suspect the entry is long overdue an overhaul.
It wouldn't occur to me to hyphenate "clothes peg" as a noun these days, and none of the up-to-date BE dictionaries that I can think of at the moment have a hyphen:
clothes peg noun a small clip made from wood or plastic used for securing clothes to a clothesline.
clothes peg [countable] British English
a wooden or plastic object that you use to fasten wet clothes to a clothesline [= clothespin American English]
(North American also clothespin)
Example of current usage:
20 PASTEL COLOUR SOFT GRIP CLOTHES PEGS
So, yes, I'd say a Wrong Entry was in order, Amy. Well spotted!