I went to Cadiz yesterday and checked HappyCow before to find vegetarian places. Although I was disappointed to see that there are no vegetarian/vegan restaurants/tapas bars in Cadiz, I wrote down La Cueva and went straight there for lunch. All the other place that I passed by were advertising pescado (fish) and jamon (ham)...
...therefore I was very happy to find out that, as far as veg-friendly goes, La Cueva is perfect. The menu (both in Spanish and in English) offers a great number of vegan and vegetarian choices (I counted 15 out of the 23 tapas of the list). Since in the menu they mark the vegetarian and vegan choices it was easy to find three vegan tapas, ask the waitress (I also asked her if those were indeed vegan, and she confirmed), and wait.
The cous cous with vegetables was yummy, with the right amount of spices. The hummus (served with crunchy bread) was also very good (with lemon on top), and the aubergines with tomato and onion (pastel de berenjenas) were great. I had a (bottled, but good) pineapple juice and I spent 9 euro in total (there was also some free bread which turned out to be perfect to eat the aubergines).
Supercheap, good food, and a great (and possbly only) choice in Cadiz for veggie people!