What do you call "candy canes" in the UK?
The one in this picture:
http://www.famouscutouts.com/candy-cane.html

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Answer

We say "candy cane" only because we don't have this tradition in the UK and so the word is a direct import with no competing word to worry about.

This is the nearest equivalent. https://en.wikipedia.org/wiki/Rock_(confectionery)
It's hardened sugar and typically has a peppermint flavour. I suspect that the product is very similar, except for the shape.

Answer

Candy Canes