This might be true in the US, but in London privately-owned sandwich shops are VERY common, there's like 6 of them within 30 seconds walk of my office. They'll typically serve mainly sandwich and wraps (made to order), or alternatively potato, pasta or rice-based meals.

There are some places that specialise in salad/veg rather than sandwiches, but they tend to be vegetarian with the only calories coming from cous cous or potato.

I'll have a look around though.