As the UK-specific requirements haven't yet been published it's difficult to be absolutely definitive as to whether Zen Cart will comply.

However, since Zen Cart uses cookies only for managing session indexes and not for storing personal information, shopping cart information (which is explicitly excluded anyway from the underlying EU directive), or any form of tracking, it's difficult to see how it could not comply.

But you would have to check cookie usage for any add-ons that you're using. The vast majority don't go anywhere near them, but a small number do. And it's not yet clear how tracking mechanisms such as Google Analytics will be treated.