Subways are everywhere and I hate them! But, they might be more your sort of thing. This is the information on their website on vegan options:
The menu items that do not contain any animal-derived ingredients are the Veggie Delite on Italian bread and the Veggie Delite salad. Also these individual items also do not contain animal-derived ingredients: all vegetables, oil, vinegar, mustard, sweet onion sauce and Fruizle. The wheat bread and deli roll contain honey but no other animal-derived ingredients.
If you're in Nottingham and can't see a Subway, just wait a while and they'll probably open one.